Exam 7: Analytic Trigonometry

Write the sum as a product. $\sin 4 x + \sin 5 x$

Solve the given equation. $\cos \theta = - \frac { \sqrt { 2 } } { 2 }$

Solve the given equation. $\sin \theta = 1$

Write the sum as a product. $\cos 4 x + \cos 5 x$

Find all solutions of $4 \sin x \cos x - 2 ( \sin x + \cos x ) + 1 = 0$ .

Solve the given equation. $\csc ^ { 2 } \theta - 2 = 0$

Verify the identity. $\cos x + \sin x \tan x = \sec x$

Verify the identity. $\sec ( - x ) - \tan ( - x ) = \sec x + \tan x$

Use a double-angle formula or a half-angle formula to simplify $2 \sin 12 \cos 12$ .

Write the sum as a product. $\sin 4 x + \sin 5 x$

Solve the given equation. $2 \sin ^ { 2 } \theta - 1 = 0$

Write $\cos ( \beta - \alpha ) \cos \alpha$ as a sum.

Use addition or subtraction formulas to find the exact value of $\cos 105 ^ { \circ }$ .

Solve the given equation. $\cos \theta = 0.25$

Use a double-angle formula or a half-angle formula to simplify $\sqrt { \frac { 1 + \cos 4 \pi } { 2 } }$ .

Solve the given equation. $\sin ^ { 2 } \theta - \sin \theta - 6 = 0$

Find $\sin 2 x$ , $\cos 2 x$ and $\tan 2 x$ , given that $\sin x = \frac { 3 } { 5 }$ and $x$ is in quadrant II.

Solve the given equation. $4 \cos ^ { 2 } \theta - 3 = 0$

Prove $\frac { \sin ( x + y ) } { \sin x \sin y } = \cot x + \cot y$ .

Solve the given equation. $\sin \theta = - \frac { \sqrt { 3 } } { 2 }$