Half Angle Formulas - How to Use (3 Examples) @MariosMathTutoring

Uploaded October 2024 | Updated September 2026, 2 weeks ago

Unlock the power of half-angle formulas to find exact trigonometric values for angles not directly on the unit circle! Mario's Math Tutoring demonstrates how to apply the half-angle identities for sine, cosine, and tangent with three detailed examples. Learn how to determine the correct sign (positive or negative) based on the original half angle's quadrant and simplify complex fractions to arrive at precise answers.

In this video, you'll discover:

0:00 Introduction to Half-Angle Formulas
0:20 Review of Half-Angle Formulas for Sine, Cosine, and Tangent
0:50 Example 1: Finding the Exact Value of sin(112.5°)
1:10 Determining the Sign (Positive/Negative) Based on the Original Angle's Quadrant
1:50 Substituting into the Half-Angle Sine Formula
2:10 Simplifying the Complex Fraction
3:00 Final Exact Value for sin(112.5°)
3:20 Example 2: Finding the Exact Value of cos(11π/12)
3:30 Converting Radians to Degrees (165°)
3:50 Determining the Sign (Positive/Negative) for cos(165°)
4:20 Substituting into the Half-Angle Cosine Formula
5:00 Simplifying the Complex Fraction
5:50 Final Exact Value for cos(11π/12)
6:10 Example 3: Finding the Exact Value of tan(105°)
6:20 Doubling the Angle to Use a Unit Circle Value (210°)
6:40 Choosing a Tangent Half-Angle Formula
7:00 Substituting Unit Circle Values for cos(210°) and sin(210°)
8:00 Simplifying the Complex Fraction and Rationalizing
Master these half-angle formulas to confidently find exact trigonometric values for a wider range of angles!

#HalfAngleFormulas #Trigonometry #ExactValues #UnitCircle #Precalculus #TrigIdentities #MathTutorial #MathHelp

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$Half Angle Formulas - How to Use (3 Examples) Unlock the power of half-angle formulas to find exact trigonometric values for angles not directly on the unit circle! Marios Math Tutoring demonstrates how to apply the half-angle identities for sine, cosine, and tangent with three detailed examples. Learn how to determine the correct sign (positive or negative) based on the original half angles quadrant and simplify complex fractions to arrive at precise answers. In this video, youll discover: 0:00 Introduction to Half-Angle Formulas 0:20 Review of Half-Angle Formulas for Sine, Cosine, and Tangent 0:50 Example 1: Finding the Exact Value of sin(112.5°) 1:10 Determining the Sign (Positive/Negative) Based on the Original Angles Quadrant 1:50 Substituting into the Half-Angle Sine Formula 2:10 Simplifying the Complex Fraction 3:00 Final Exact Value for sin(112.5°) 3:20 Example 2: Finding the Exact Value of cos(11π/12) 3:30 Converting Radians to Degrees (165°) 3:50 Determining the Sign (Positive/Negative) for cos(165°) 4:20 Substituting into the Half-Angle Cosine Formula 5:00 Simplifying the Complex Fraction 5:50 Final Exact Value for cos(11π/12) 6:10 Example 3: Finding the Exact Value of tan(105°) 6:20 Doubling the Angle to Use a Unit Circle Value (210°) 6:40 Choosing a Tangent Half-Angle Formula 7:00 Substituting Unit Circle Values for cos(210°) and sin(210°) 8:00 Simplifying the Complex Fraction and Rationalizing Master these half-angle formulas to confidently find exact trigonometric values for a wider range of angles! #HalfAngleFormulas #Trigonometry #ExactValues #UnitCircle #Precalculus #TrigIdentities #MathTutorial #MathHelp * Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below) https://www.mariosmathtutoring.com/free-math-videos.html ➡️JOIN the channel as a CHANNEL MEMBER at the ADDITIONAL VIDEOS level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join$

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