Videos

Video thumbnail for Simplifying Trigonometric Expressions | Fundamental Trigonometric Identities | Formulas | Problems
13:19
Icon for www.youtube.comyoutube.com › watch

Simplifying Trigonometric Expressions | Fundamental Trigonometric Identities | Formulas | Problems

Pre-Calculus Simplifying Trigonometric Expressions | Fundamental Trigonometric Identities | Formulas | Problems The fundamental trig identities are used to establish other relationships among trigonometric functions. To verify an identity we show that one side of the identity can be simplified so that is identical to the other side. Each side ...
YouTube
· Jun 21, 2021
Video thumbnail for Trigonometry - Checking trig identities using a calculator
06:14
Icon for www.youtube.comyoutube.com › watch

Trigonometry - Checking trig identities using a calculator

When working with trig identities it can be difficult to tell if you have an equivalent expression. Fortunately your calculator can help in this process. Watch this video to see how you can use the calculator to check trig identities. For more videos please visit http://www.mysecretmathtutor.com
YouTube
· Sep 25, 2016
Video thumbnail for How do you simplify trigonometric expressions
08:06
Icon for www.youtube.comyoutube.com › watch

How do you simplify trigonometric expressions

👉 Learn how to verify trigonometric identities having rational expressions. To verify trigonometric expression means to verify that the terms on the left-hand side of the equality sign is equal to the terms on the right-hand side. To verify rational trigonometric identities, it is usually more convenient to start with getting rid of the ...
YouTube
· Nov 25, 2013
Video thumbnail for Simplifying trigonometric expressions by using pythagorean identities
05:22
Icon for www.youtube.comyoutube.com › watch

Simplifying trigonometric expressions by using pythagorean identities

👉 Learn how to verify trigonometric identities having rational expressions. To verify trigonometric expression means to verify that the terms on the left-hand side of the equality sign is equal to the terms on the right-hand side. To verify rational trigonometric identities, it is usually more convenient to start with getting rid of the ...
YouTube
· Jan 4, 2013
Video thumbnail for Power Reducing Formulas - Trigonometric Identities
10:07
Icon for www.youtube.comyoutube.com › watch

Power Reducing Formulas - Trigonometric Identities

This trigonometry video tutorial explains how to use power reducing formulas to simplify trigonometric expressions. It contains the power reducing trigonometric identities for sine, cosine, and tangent. Examples and practice problems include sin^4(x), sin^2(x)cos^2(x), and sin^4(x)cos^2(x). Trigonometry - Free Formula Sheet: https://www.video ...
YouTube
· Nov 8, 2016
Video thumbnail for Introduction to Using Trigonometric Identities (Precalculus - Trigonometry 23)
23:44
Icon for www.youtube.comyoutube.com › watch

Introduction to Using Trigonometric Identities (Precalculus - Trigonometry 23)

A quick look at Trig Identities and how to use them. Basic identities such as the Pythagorean Identity, Reciprocal Identities, and Even/Odd Identities are explored. Support: https://www.patreon.com/ProfessorLeonard
YouTube
· Sep 8, 2021
Video thumbnail for Verifying a trigonometric Identities
05:12
Icon for www.youtube.comyoutube.com › watch

Verifying a trigonometric Identities

👉 Learn how to verify rational trigonometric identities involving the addition and subtraction of terms. To verify trigonometric expression means to verify that the term on the left-hand side of the equality sign is equal to the term on the right-hand side. To verify rational trigonometric identities, it is usually more convenient to start ...
YouTube
· Dec 18, 2012
Video thumbnail for Product To Sum Identities and Sum To Product Formulas - Trigonometry
13:25
Icon for www.youtube.comyoutube.com › watch

Product To Sum Identities and Sum To Product Formulas - Trigonometry

This trigonometry video tutorial explains how to simplify trigonometric expressions using the product to sum identities and how to find the exact value of trigonometric expressions using the sum to product formulas. Trigonometry - Free Formula Sheet: https://www.video-tutor.net/formula-sheets.html _____________________________ Bearing Problems ...
YouTube
· Oct 20, 2017
Video thumbnail for How to Prove Trigonometric Identities (Precalculus - Trigonometry 24)
55:39
Icon for www.youtube.comyoutube.com › watch

How to Prove Trigonometric Identities (Precalculus - Trigonometry 24)

A very in-depth look at proving trigonometric identities. Several techniques are explored in many different examples of solving trig functions. Support: https://www.patreon.com/ProfessorLeonard
YouTube
· Sep 20, 2021
Video thumbnail for Simplifying Trigonometric Expressions (Using Identities)
11:29
Icon for www.youtube.comyoutube.com › watch

Simplifying Trigonometric Expressions (Using Identities)

How to work with Trigonometric Identities. We discuss the reciprocal identities, quotient identities, pythagorean identities, cofunctions, and even and odd identities. 0:08 What is a Trig Identity 0:26 Formulas for Reciprocal Identities 0:44 Pythagorean Identities 1:17 CoFunction Identities 1:37 Even and Odd Identities 2:13 Understanding the ...
YouTube
· Feb 1, 2016
Video thumbnail for Trig Identities
27:57
Icon for www.youtube.comyoutube.com › watch

Trig Identities

This trigonometry video tutorial discusses common trig identities and formulas such as the Pythagorean identities, reciprocal identities, quotient identities, even odd identities, cofunction identities, double angle formulas, half angle formulas, sum and difference identities, power reducing formulas, product to sum identities, and sum to ...
YouTube
· Apr 6, 2023
Video thumbnail for Solving Trigonometric Equations Using Identities, Multiple Angles, By Factoring, General Solution
13:52
Icon for www.youtube.comyoutube.com › watch

Solving Trigonometric Equations Using Identities, Multiple Angles, By Factoring, General Solution

This trigonometry video tutorial shows you how to solve trigonometric equations using identities with multiple angles, by factoring, and by finding the general solution. This video contains plenty of examples and practice problems. Trigonometry - Free Formula Sheet: https://www.video-tutor.net/formula-sheets.html Trigonometry Video Lessons ...
YouTube
· Feb 22, 2016
Video thumbnail for Pythagorean Identities - Examples & Practice Problems, Trigonometry
07:43
Icon for www.youtube.comyoutube.com › watch

Pythagorean Identities - Examples & Practice Problems, Trigonometry

This trigonometry video tutorial provides a basic introduction into the Pythagorean identities of trigonometric functions. it provides plenty of examples and practice problems of evaluating cosine given the value of sine. Trigonometry - Free Formula Sheet: https://www.video-tutor.net/formula-sheets.html Trigonometry Video Lessons: https://www ...
YouTube
· Oct 13, 2017
Video thumbnail for Lesson 1 - Basic Trig Identities Involving Sin, Cos, and Tan
21:24
Icon for www.youtube.comyoutube.com › watch

Lesson 1 - Basic Trig Identities Involving Sin, Cos, and Tan

This is just a few minutes of a complete course. Get full lessons & more subjects at: http://www.MathTutorDVD.com. Basic trig identities are the core trig identities that involve sine, cosine, tangent, cotangent, secant, and cosecant. We discuss each of these important trigonometric functions and gain practice solving problems. We will first ...
YouTube
· Feb 3, 2016
Video thumbnail for Calculator Techniques FOR BOARD EXAM - Evaluating Functions and Simplifying Expressions 10 EXAMPLES
47:22
Icon for www.youtube.comyoutube.com › watch

Calculator Techniques FOR BOARD EXAM - Evaluating Functions and Simplifying Expressions 10 EXAMPLES

Donate via G-cash: 09568754624 Caltech playlist: https://www.youtube.com/watch?v=Ljb9r6gXWa4&list=PL_NkZ6-1skgkfIob6KqRruNBM2CcHoyuc This video will help teach you how to use calculator techniques in order to evaluate a function with a single or double variable as well as simplifying expressions. This video contains numerous examples that will ...
YouTube
· Jan 7, 2021
Video thumbnail for Double Angle Identities & Formulas of Sin, Cos & Tan - Trigonometry
18:16
Icon for www.youtube.comyoutube.com › watch

Double Angle Identities & Formulas of Sin, Cos & Tan - Trigonometry

This trigonometry video tutorial provides a basic introduction to the double angle identities of sine, cosine, and tangent. It explains how to derive the double angle formulas from the sum and difference identities of sin, cos, and tan and how to use the double angle formulas to find the exact value of trigonometric expressions using right ...
YouTube
· Oct 19, 2017
Video thumbnail for Simplifying Trigonometric Expressions
12:15
Icon for www.youtube.comyoutube.com › watch

Simplifying Trigonometric Expressions

This trigonometry video tutorial explains how to simplify trigonometric expressions using reciprocal identities and Pythagorean identities. Trigonometry - Free Formula Sheet: https://www.video-tutor.net/formula-sheets.html Final Exam and Test Prep Videos: https://bit.ly/41WNmI9 ...
YouTube
· Feb 16, 2022
Video thumbnail for Verifying Trigonometric Identities
09:14
Icon for www.youtube.comyoutube.com › watch

Verifying Trigonometric Identities

Verifying trigonometric identities can be super fun! And also very frustrating when you can't figure them out. It can be tricky because there's no precise way to go about doing this, you have to just use your intuition, but let's go over some common strategies and identities that will more than likely use at one point or another! Watch the ...
YouTube
· Jan 22, 2018
Video thumbnail for Verifying Trigonometric Identities
24:51
Icon for www.youtube.comyoutube.com › watch

Verifying Trigonometric Identities

This trigonometry video tutorial focuses on verifying trigonometric identities with hard examples including fractions. It contains plenty of examples and practice problems. This video tutorial contains plenty of tips and tricks that will help you on your homework or upcoming worksheet assignment. It explains when to convert secant and tangent ...
YouTube
· Jan 10, 2021
Video thumbnail for Verifying trigonometric identities, hard with multiple steps
06:53
Icon for www.youtube.comyoutube.com › watch

Verifying trigonometric identities, hard with multiple steps

👉 Learn how to verify rational trigonometric identities involving the addition and subtraction of terms. To verify trigonometric expression means to verify that the term on the left-hand side of the equality sign is equal to the term on the right-hand side. To verify rational trigonometric identities, it is usually more convenient to start ...
YouTube
· Jan 22, 2013
Video thumbnail for GCSE Maths - How to Prove Algebraic Identities - Proof Part 2
04:37
Icon for www.youtube.comyoutube.com › watch

GCSE Maths - How to Prove Algebraic Identities - Proof Part 2

⭐️ https://www.cognito.org/ ⭐️ *** WHAT'S COVERED *** 1. Understanding Algebraic Identities. 2. Rules for Working with Identities. 3. Method for Proving Algebraic Identities. * Manipulating one side algebraically until it is identical to the other side. * Using techniques like expanding brackets, simplifying by collecting like terms ...
YouTube
· Sep 24, 2020
Video thumbnail for Simplifying Trigonometric Expressions
14:50
Icon for www.youtube.comyoutube.com › watch

Simplifying Trigonometric Expressions

This MATHguide video demonstrates how to simplify trigonometric expressions and verify trigonometric equations. See our text lesson on this topic at http://www.mathguide.com/lessons2/TrigExpress.html.
YouTube
· Mar 27, 2015
Video thumbnail for Solving Trigonometric Equations By Factoring & By Using Double Angle Identities
18:32
Icon for www.youtube.comyoutube.com › watch

Solving Trigonometric Equations By Factoring & By Using Double Angle Identities

This trigonometry video tutorial explains how to solve trigonometric equations by factoring and by using double angle formulas and identities. It explains how to factor trigonometric expressions using the difference of perfect squares method and the same techniques used to factor trinomials in algebra. Trigonometry - Free Formula Sheet: https ...
YouTube
· Oct 21, 2017
Video thumbnail for Limits of Trigonometric Functions
15:23
Icon for www.youtube.comyoutube.com › watch

Limits of Trigonometric Functions

This calculus video tutorial provides a basic introduction into evaluating limits of trigonometric functions such as sin, cos, and tan. It contains plenty of practice problems. Limits - Free Formula Sheet: https://www.video-tutor.net/calculus-formula-sheets.html Limits - Video Lessons: https://www.video-tutor.net/limits.html Final Exam and Test ...
YouTube
· Feb 21, 2018
Video thumbnail for Indefinite Integral - Basic Integration Rules, Problems, Formulas, Trig Functions, Calculus
29:00
Icon for www.youtube.comyoutube.com › watch

Indefinite Integral - Basic Integration Rules, Problems, Formulas, Trig Functions, Calculus

This calculus video tutorial explains how to find the indefinite integral of a function. It explains how to apply basic integration rules and formulas to help you integrate functions. Calculus 1 Final Exam Review: https://www.video-tutor.net/calculus-1-final.html Integration - Free Formula Sheet: https://www.video-tutor.net/calculus-formula ...
YouTube
· Dec 20, 2016
Video thumbnail for Solving Logarithmic Equations
25:27
Icon for www.youtube.comyoutube.com › watch

Solving Logarithmic Equations

This algebra video tutorial explains how to solve logarithmic equations with logs on both sides. It explains how to convert from logarithmic form to exponential form using basic properties of logarithms. This video includes examples and practice problems with natural logarithms as well. Logarithmic - Free Formula Sheet: https://www.video-tutor ...
YouTube
· Feb 1, 2018
Video thumbnail for Polynomials - Adding, Subtracting, Multiplying and Dividing Algebraic Expressions
17:53
Icon for www.youtube.comyoutube.com › watch

Polynomials - Adding, Subtracting, Multiplying and Dividing Algebraic Expressions

This algebra video tutorial explains how to simplify algebraic expressions by adding and subtracting polynomials. It shows you how to distribute constants to polynomial expressions and how to add and subtract / combine like terms to simplify the polynomial expression. It also contains examples multiplying and dividing polynomial expressions. it ...
YouTube
· Jan 10, 2017
Video thumbnail for How to Simplify an Expression: A Beginner's Guide | Algebraic Expressions | Math with Mr. J
55:18
Icon for www.youtube.comyoutube.com › watch

How to Simplify an Expression: A Beginner's Guide | Algebraic Expressions | Math with Mr. J

Welcome to How to Simplify an Expression with Mr. J! Need help with how to simplify algebraic expressions? You're in the right place! Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with simplifying algebraic expressions. Mr. J will go through examples of how to simplify ...
YouTube
· Mar 1, 2023
Video thumbnail for Logic Gates, Truth Tables, Boolean Algebra AND, OR, NOT, NAND & NOR
54:07
Icon for www.youtube.comyoutube.com › watch

Logic Gates, Truth Tables, Boolean Algebra AND, OR, NOT, NAND & NOR

This electronics video provides a basic introduction into logic gates, truth tables, and simplifying boolean algebra expressions. It discusses logic gates such as the AND, OR, NOT, NAND and NOR Gates. This video is for college students who are taking introduction to logic design. Full 2 Hour Video on YouTube: https://www.youtube.com/watch?v ...
YouTube
· Jan 22, 2021
Video thumbnail for Simplifying Rational Expressions
11:08
Icon for www.youtube.comyoutube.com › watch

Simplifying Rational Expressions

This algebra video tutorial explains how to simplify rational expressions with variables, exponents & fractions by expanding, factoring and canceling. Algebra - Free Formula Sheets: https://bit.ly/3CBeZMY _________________________________ Fundamental Theorem of Algebra: https://www.youtube.com/watch?v=cAfRgqEOURw Rational Expressions - Basic ...
YouTube
· Jan 22, 2018
Video thumbnail for Trigonometric Substitution
19:50
Icon for www.youtube.comyoutube.com › watch

Trigonometric Substitution

This calculus video tutorial provides a basic introduction into trigonometric substitution. It explains when to substitute x with sin, cos, or sec. It also explains how to perform a change of variables using u-substitution integration techniques and how to use right triangle trigonometry with sohcahtoa to convert back from angles in the form of ...
YouTube
· Mar 26, 2021
Video thumbnail for Fractional Exponents
11:32
Icon for www.youtube.comyoutube.com › watch

Fractional Exponents

This algebra 2 video tutorial explains how to simplify fractional exponents including negative rational exponents and exponents in radicals with variables. It provides practice problems and examples of multiplying and dividing radical expressions with different index numbers followed by simplifying the remaining expression. Exponents - Free ...
YouTube
· Feb 7, 2017
Video thumbnail for Summation Formulas and Sigma Notation - Calculus
20:24
Icon for www.youtube.comyoutube.com › watch

Summation Formulas and Sigma Notation - Calculus

This calculus video tutorial provides a basic introduction into summation formulas and sigma notation. It explains how to find the sum using summation formulas for constants, i, i^2, and i^3. Integration - Free Formula Sheet: https://www.video-tutor.net/calculus-formula-sheets.html Calculus 1 Final Exam Review: https://www.youtube.com/watch?v ...
YouTube
· Mar 9, 2018
Video thumbnail for Example 1: Simplifying polynomials | Algebra I | Khan Academy
03:37
Icon for www.youtube.comyoutube.com › watch

Example 1: Simplifying polynomials | Algebra I | Khan Academy

Simplify 3x^2 - 8x + 7 + 2x^3 - x^2 + 8x - 3 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/polynomial-basics-core-algebra/e/adding_and_subtracting_polynomials?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Watch the next lesson: https://www ...
YouTube
· Jan 27, 2011
Video thumbnail for GCSE Maths - How to Simplify Algebraic Expressions
06:27
Icon for www.youtube.comyoutube.com › watch

GCSE Maths - How to Simplify Algebraic Expressions

⭐️ https://www.cognito.org/ ⭐️ *** WHAT'S COVERED *** 1. Simplifying algebraic expressions involving multiplication. 2. Using indices (powers) to simplify repeated variables. 3. Multiplying numerical coefficients together. 4. Combining variables using the rules of indices. 5. How to handle negative numbers when simplifying. 6. Expanding ...
YouTube
· Jun 8, 2020
Video thumbnail for Karnaugh Maps – Simplify Boolean Expressions
07:26
Icon for www.youtube.comyoutube.com › watch

Karnaugh Maps – Simplify Boolean Expressions

This video follows on from the previous videos about Karnaugh maps. It explains how Karnaugh maps, and truth tables, can be used to simplify complex Boolean expressions.
YouTube
· Jul 16, 2016
Video thumbnail for Simplify 24 Trigonometric Expressions With Identities
27:55
Icon for www.youtube.comyoutube.com › watch

Simplify 24 Trigonometric Expressions With Identities

In this video we will explore 24 different trigonometric expressions for to simplify. To Simplify we will use algebraic processes as well as trigonometric identities. Corrections: 24:13 In Example #20, sec^2x is equal to (tan^2x + 1). So final answer: -5(tanx-secx) 25:15 In Example #21, final answer is cos^2 and not tan^2 Want my resources ...
YouTube
· May 14, 2020
Video thumbnail for How to Simplify Fractions on a Calculator
01:31
Icon for www.youtube.comyoutube.com › watch

How to Simplify Fractions on a Calculator

YouTube
· Apr 13, 2015
Video thumbnail for How to Simplify Trigonometric Expressions Using Trig Identities
14:13
Icon for www.youtube.comyoutube.com › watch

How to Simplify Trigonometric Expressions Using Trig Identities

This trigonometry or precalculus lesson is showing you how to simplify trig expressions using trigonometric identities. In solving this math problems in trigonometry, it is important that you have the trig identities or formula so you can modify some of the trig functions into terms that you can simplify. Your skills in factoring some ...
YouTube
· Mar 8, 2018
Video thumbnail for How to expand polynomials using calculator
12:01
Icon for www.youtube.comyoutube.com › watch

How to expand polynomials using calculator

Math is so much easy when you know these calculator tips and tricks. No need to perform hand calculations or when you wanna double check your answers, ONLY hit this once and boom, there you go! "Nothing is hard when STEM-Solver is here!" 👉 If you enjoy or learn something new today, give it a LIKE 👍 SHARE and SUBSCRIBE to my channel so ...
YouTube
· Jan 16, 2023
Video thumbnail for Factor and use fundamental identities to simplify
03:04
Icon for www.youtube.comyoutube.com › watch

Factor and use fundamental identities to simplify

👉 Learn how to simplify identities by factoring. Just like in normal algebraic expressions, trigonometric identities can be simplified by factoring out the GCFs from the terms of the identities, then common trigonometric identities like the quotient, reciprocal, even, odd, co-function, and the Pythagoras trigonometric identities can be ...
YouTube
· Dec 17, 2012
Video thumbnail for Addition and subtraction and use fundamental identities
05:49
Icon for www.youtube.comyoutube.com › watch

Addition and subtraction and use fundamental identities

👉 Learn how to simplify rational identities involving addition and subtraction. To simplify rational identities involving addition and subtraction, first, we find the LCM of the denominators which most time is the product of the terms in the denominators. After we have found the LCM of the denominators, we next, multiply the numerator and ...
YouTube
· Dec 18, 2012
Video thumbnail for Ep 034: Basic Boolean Algebraic Simplification Examples
18:20
Icon for www.youtube.comyoutube.com › watch

Ep 034: Basic Boolean Algebraic Simplification Examples

Join us as we simplify a few Boolean algebraic expressions. Takeaways: At the completion of this lesson, each student should be able to apply the identities and properties of Boolean algebra to perform basic simplifications of Boolean algebraic expressions. #boolean #algebra #simplification
YouTube
· Aug 27, 2020
Video thumbnail for Proving Trigonometric Identities with Simplification
00:59
Icon for www.tiktok.comtiktok.com › @ElectricalMath

Proving Trigonometric Identities with Simplification

Learn how to prove trigonometric identities by simplifying complex expressions to reveal their identities. #math #trigonometry #proof ElectricalMath(@electricalmath). original sound - ElectricalMath. A classic example of a trigonometric identity proof. The idea is to start with the more complicated side and try to simplify it down to the ...
TikTok
· Jan 22, 2025
Video thumbnail for TI84 Calculator-Simplifying Expressions
07:50
Icon for www.youtube.comyoutube.com › watch

TI84 Calculator-Simplifying Expressions

This is an educational video about the TI-84 calculator. It teaches: How to verify you have simplified an expression correctly
YouTube
· Mar 23, 2023
Video thumbnail for Can you simplify without a Calculator? | (Exponents) | #math #maths
03:25
Icon for www.youtube.comyoutube.com › watch

Can you simplify without a Calculator? | (Exponents) | #math #maths

Learn how to simplify the problem without a calculator. Step-by-step tutorial by PreMath.com Today I will teach you tips and tricks to solve the given math question in a simple and easy way. Learn how to solve math puzzles fast! Fast and easy explanation by PreMath.com https://youtu.be/yR_kzZLX97k Need help with solving this Math Olympiad ...
YouTube
· 20 days ago
Video thumbnail for Learn how to simplify functions
00:50
Icon for www.youtube.comyoutube.com › watch

Learn how to simplify functions

👉 Learn how to multiply two functions. We will explore the multiplication of linear, quadratic, rational, and radical functions. To multiply two functions, we simply algebraically multiply the rules (contents) of the two functions. We will then simplify the product and determine the domain. 👏SUBSCRIBE to my channel here: https://www ...
YouTube
· Aug 21, 2016
Video thumbnail for Simplify Trig Identities (FULL LESSON)
01:24:03
Icon for www.youtube.comyoutube.com › watch

Simplify Trig Identities (FULL LESSON)

Looking to learn all about Trigonometric Identities? This full lesson will give full leson on what are trigonometric identities and how to simplify them. Download the document and work through it on your own or work through it with me. 📂 Download worksheet here - ⭐️ Practice Basic Trigonometric Identities - Pre-Calculus Full Lessons ...
YouTube
· Feb 23, 2025
Video thumbnail for Algebra EOC: Ep. 48 Simplifying Functions Q2
03:41
Icon for www.youtube.comyoutube.com › watch

Algebra EOC: Ep. 48 Simplifying Functions Q2

Dr. Michelle Ihrig is Dr. Test Prep. In this video, Dr. Ihrig shows how to use the Desmos graphing calculator as a tool to solve EOC-style questions. Resources: GA Practice Portal: https://wbte.drcedirect.com/GA/portals/ga Desmos Calculator: https://www.desmos.com/practice
YouTube
· Nov 30, 2023
Video thumbnail for Simplify SAT Math- No Calculator #short #algebra #shorts #satmath
01:08
Icon for www.youtube.comyoutube.com › watch

Simplify SAT Math- No Calculator #short #algebra #shorts #satmath

Simplify SAT Math- No Calculator #short #algebra #shorts #satmath This Short is all about how to simplify rational expression using algebraic identities and exponent laws. If you find this short video useful please do subscribe our channel. Thanks a lot for watching and motivating us. #algebra #math #rational #expression #short #shorts #satmath
YouTube
· 28 days ago