3.6 Trigonometric identities Quiz

1. $\theta$ is in the fourth quadrant and $\cos\theta = \frac{8}{17}$. Find $\sin\theta$.

• A. $\frac{15}{17}$
• B. $-\frac{15}{17}$
• C. $-\frac{9}{17}$
• D. $\frac{9}{17}$

2. Given $\sin x = \frac{2}{3}$, find $\cos 2x$.

• A. $\frac{1}{9}$
• B. $-\frac{1}{9}$
• C. $\frac{4}{3}$
• D. $\frac{5}{9}$

3. Which expression is equal to $\cos^2 x - \sin^2 x$?

• A. $1$
• B. $\cos 2x$
• C. $\sin 2x$
• D. $2\cos x$

4. $x$ is acute and $\tan x = \frac{3}{4}$. Find $\sin 2x$.

• A. $\frac{12}{25}$
• B. $\frac{6}{5}$
• C. $\frac{24}{25}$
• D. $\frac{7}{25}$

5. Simplify $\frac{1 - \cos 2x}{\sin 2x}$.

• A. $\cos x$
• B. $\tan x$
• C. $\sin x$
• D. $2\tan x$