Exam 6: Analytic Trigonometry

Use substitution to determine whether the given x-value is a solution of the equation. Find All Solutions of a Trigonometric Equation - $\tan x = \frac { \sqrt { 3 } } { 3 } , x = \frac { 7 \pi } { 6 }$

Use the given information to find the exact value of the trigonometric function. - $\cos \theta = \frac { 1 } { 4 } , \csc \theta > 0 \quad$ Find $\sin \frac { \theta } { 2 }$ .

Solve the equation on the interval [0, 2π). - $2 \sin ^ { 2 } x = \sin x$

Use substitution to determine whether the given x-value is a solution of the equation. Find All Solutions of a Trigonometric Equation - $7 \cos x + 8 \sqrt { 2 } = 5 \cos x + 7 \sqrt { 2 }$

Use the graph to complete the identity. - $\sin 6 x \cos 3 x - \cos 6 x \sin 3 x = ?$

Use the figure to find the exact value of the trigonometric function. -Find $\sin 2 \theta$ .

Use the Formula for the Cosine of the Difference of Two Angles - $\cos \left( 155 ^ { \circ } \right) \cos \left( 35 ^ { \circ } \right) + \sin \left( 155 ^ { \circ } \right) \sin \left( 35 ^ { \circ } \right)$

Find the exact value under the given conditions. - $\cos \alpha = - \frac { 24 } { 25 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\tan ( \alpha + \beta )$

Use Sum and Difference Formulas for Cosines and Sines - $\cos 285 ^ { \circ }$

Express the sum or difference as a product. - $\cos 2 x - \cos 4 x$

Solve the problem. -If a projectile is fired at an angle $\theta$ and initial velocity $v$ , then the horizontal distance traveled by the projectile is given by $D = \frac { 1 } { 16 } \mathrm { v } ^ { 2 } \sin \theta \cos \theta$ . Express $D$ as a function of $2 \theta$ .

Express the sum or difference as a product. - $\sin 4 x - \sin 6 x$

Solve the equation on the interval [0, 2π). - $\cos x = \sin x$

Use the given information to find the exact value of the expression. - $\sin \alpha = \frac { 3 } { 5 } , \alpha$ lies in quadrant II, and $\cos \beta = \frac { 2 } { 5 } , \beta$ lies in quadrant I $\quad$ Find $\cos ( \alpha - \beta )$ .

Use the given information to find the exact value of the trigonometric function. - $\sin \theta = \frac { 1 } { 4 } , \theta$ lies in quadrant I $\quad$ Find $\sin \frac { \theta } { 2 }$

Use Sum and Difference Formulas for Cosines and Sines - $\sin 260 ^ { \circ } \cos 20 ^ { \circ } - \cos 260 ^ { \circ } \sin 20 ^ { \circ }$

Describe the graph using another equation. - $y=\sin (\pi-x)$

Complete the identity. - $\frac { \cos x - \sin x } { \cos x } + \frac { \sin x - \cos x } { \sin x } = ?$

Use the Formula for the Cosine of the Difference of Two Angles - $\cos \left( 255 ^ { \circ } - 15 ^ { \circ } \right)$

Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. - $\sin 2 x + \sin 4 x = \sin 5 x$