Double Angle Formulas - How to Use (2 Examples) @MariosMathTutoring

Uploaded October 2024 | Updated September 2026, 2 weeks ago

Unlock the power of double angle formulas for sine, cosine, and tangent in this comprehensive trigonometry tutorial! We'll work through two key examples: one where you'll calculate sin(2θ), cos(2θ), and tan(2θ) given sin(θ) and a quadrant restriction, and another where you'll solve a trigonometric equation using these powerful identities.

Double angle formulas are essential tools for simplifying expressions and solving equations in trigonometry and precalculus. You'll learn how to apply these identities strategically to transform expressions involving 2θ into expressions with just θ, making complex problems much more manageable.

In this video, you'll learn:

The double angle formulas for sine, cosine (all three variations), and tangent.
How to use a given trigonometric ratio and quadrant to find missing side lengths of a right triangle.
Step-by-step calculations for sin(2θ), cos(2θ), and tan(2θ).
How to strategically choose the correct cosine double angle formula for equation solving.
Solving trigonometric equations by transforming double angles into single angles.
Factoring quadratic-like trigonometric equations.
Finding general solutions for trigonometric equations using the unit circle.
Timestamps:

0:00 Introduction to Double Angle Formulas
0:30 Example 1: Calculating sin(2θ), cos(2θ), tan(2θ) given sin(θ) and a Quadrant
1:00 Drawing the Triangle and Finding Missing Sides in the Correct Quadrant
2:10 Applying the Double Angle Formula for Sine (sin(2θ))
3:30 Applying a Double Angle Formula for Cosine (cos(2θ)) - Choosing the Best Option
5:50 Applying the Double Angle Formula for Tangent (tan(2θ)) - Two Methods
8:50 Example 2: Solving a Trigonometric Equation Using Double Angle Formulas
9:40 Strategically Choosing the Cosine Double Angle Formula
10:40 Rewriting the Equation as a Quadratic in terms of Cosine
11:30 Factoring the Quadratic Trigonometric Equation
12:40 Solving for x using the Unit Circle
13:40 Finding the General Solution
14:50 Conclusion & More Practice Resources
Master these double angle formulas to boost your trigonometry skills! If you found this video helpful, please give it a thumbs up and subscribe to Mario's Math Tutoring for more precalculus and trigonometry lessons!

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