Practice Double-Angle Identities in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Formulas expressing \sin(2\theta), \cos(2\theta), and \tan(2\theta) in terms of single-angle trig functions.
What if both angles in the sum formula are the same? Setting A = B = \theta in the sum identities gives you the double-angle formulas. They answer: if you know the trig values for an angle, what are the trig values for twice that angle? The cosine double-angle formula is especially versatile because it has three equivalent forms, each useful in different situations—pick whichever one simplifies your problem.
Example 1
easyIf \cos(\theta) = \frac{3}{5}, find \cos(2\theta) using the double-angle formula.
Example 2
mediumFind \sin(2\theta) given that \tan(\theta) = \frac{5}{12} and \theta is in Quadrant I.
Example 3
mediumSimplify \cos^2(x) - \sin^2(x) using a double-angle identity.
Example 4
hardSolve \sin(2x) = \cos(x) for x \in [0, 2\pi).