Exam 5: Analytic Trigonometry

Use the figure to find the exact value of the trigonometric function. Cos 2 $\theta$ a = 1, b = 2

Evaluate the following expression.(x $\neq$ $\pi$ /2 + $\pi$ n, where n is a whole number) $\frac { 11 \cos \left[ \frac { \pi } { 2 } - x \right] } { \sin \left[ \frac { \pi } { 2 } - x \right] }$

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $0 < x < \frac { \pi } { 2 }$ . $\sqrt { x ^ { 2 } + 25 } , x = 5 \tan \theta$

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 7 } { 25 }$ and $\cos v = - \frac { 12 } { 13 }$ .(Both u and v are in Quadrant II.)

Evaluate the following expression.(x $\neq$ $\pi$ n, where n is a whole number) $5 \sec ^ { 2 } \left( \frac { \pi } { 2 } - x \right) - 5$

Find all solutions of the following equation in the interval [0, 2 $\pi$ ). $15 \tan ^ { 3 } x = 5 \tan x$

Use a double-angle formula to find the exact value of cos2u when $\sin u = \frac { 7 } { 25 } \text {, where } \frac { \pi } { 2 } < u < \pi$

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\cot ^ { 2 } \alpha - \cot ^ { 2 } \alpha \cos ^ { 2 } \alpha$

Find the expression as the cosine of an angle. $\cos \frac { \pi } { 5 } \cos \frac { \pi } { 3 } - \sin \frac { \pi } { 5 } \sin \frac { \pi } { 3 }$

Evaluate the following expression. ​ 4 tan t cot t ​

Use the figure to find the exact value of the trigonometric function. Sec 2 $\theta$ a = 1, b = 8

Write the given expression as the sine of an angle. $\sin 85 ^ { \circ } \cos 50 ^ { \circ } - \sin 50 ^ { \circ } \cos 85 ^ { \circ }$

Use the figure to find the exact value of the trigonometric function. Cot 2 $\theta$ a = 1, b = 6

Use a double-angle formula to rewrite the expression. ​ 2 sin² x - 1 ​

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $0 < x < \frac { \pi } { 2 }$ . $\sqrt { 16 - x ^ { 2 } } , x = 4 \cos \theta$

If x = 2 tan $\theta$ , use trigonometric substitution to write $\sqrt { 4 + x ^ { 2 } }$ as a trigonometric function of $\theta$ , where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .

Use the sum-to-product formulas to rewrite the sum or difference as a product. Cos 3 $\theta$ + cos 8 $\theta$

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ .Then find sin $\theta$ and cos $\theta$ . $4 = \sqrt { 16 - x ^ { 2 } } , x = 4 \sin \theta$

If x = 5 sin $\theta$ , use trigonometric substitution to write $\sqrt { 25 - x ^ { 2 } }$ as a trigonometric function of $\theta$ , where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .

Use a double-angle formula to rewrite the expression. ​ 3 - 6 sin² x ​