Exam 5: Analytic Trigonometry

Find the area. Round your answer to the nearest hundredth if necessary. -Find the area of the triangle with the following measurements: $C = 107 ^ { \circ } , a = 2.4$ in., $b = 4.7$ in.

Complete the identity. -The expression $\frac { \cot \alpha + \csc \alpha } { \sin \alpha + \tan \alpha }$ is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be u: the right hand side of the equation to complete the identity?

Determine if the following is an identity. - $\frac { \cot ^ { 2 } x } { \csc x - 1 } = \frac { 1 + \sin x } { \sin x }$

Use basic identities to simplify the expression. - $\tan ^ { 2 } \theta \csc ^ { 2 } \theta$

Express the function as a sinusoid of the form y = a sin (bx + c). - $y = 7 \sin x - 2 \cos x$

Find an exact value. - $\cos 75 ^ { \circ }$

Solve the problem. -A ship travels 61 km on a bearing of 17°, and then travels on a bearing of 107° for 161 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.

Find all solutions to the equation in the interval [0, 2). - $\cos x = \sin 2 x$

Prove the identity. -sin 4x = 2 sin 2x cos 2x

Find an exact value. - $\tan \frac { 7 \pi } { 12 }$

Simplify the expression. - $\cos x + \sin x \tan x$

Solve. -Lookout station B is located 13 mi due east of station A. The bearing of a fire from A is $S 11 ^ { \circ } 30 ^ { \prime } W$ and the bearing from $B$ is $S 40 ^ { \circ } 40 ^ { \prime } \mathrm { W }$ . Determine the distance from the fire to $B$ (to the nearest tenth of a mile).

Complete the identity. -The expression $\frac { \cos \theta - \sin ^ { 2 } \theta } { \cos \theta } \cdot \csc \theta$ is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be u: the right hand side of the equation to complete the identity?

Find all solutions to the equation. - $4 \sin ^ { 2 } x - 4 \sin x + 1 = 0$

Prove the identity. - $\csc ^ { 4 } x - \cot ^ { 4 } x = \csc ^ { 2 } x + \cot ^ { 2 } x$

Write each expression in factored form as an algebraic expression of a single trigonometric function. - $\tan ^ { 4 } x - \sec ^ { 4 } x$

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. - $\mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 44 , \mathrm {~b} = 49$

Solve the triangle. - $\mathrm { A } = 34 ^ { \circ } , \mathrm { B } = 68 ^ { \circ } , \mathrm { b } = 6$

Simplify the expression. - $\frac { \sec x } { \sin x } - \frac { \cos x } { \sin x }$

Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. -a = 66 b = 65.4 C = 42.7