Exam 6: Trigonometric Functions: Unit Circle Approach

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $a = 101 , \quad b = 81 , \quad \angle A = 135 ^ { \circ }$

Two cities in the western hemisphere lie approximately on the same meridian. Guatemala city has latitude of $15.5 ^ { \circ }$ N and Baton Rouge, Louisiana $30.5 ^ { \circ }$ N. Find the distance between these two cities. (The radius of the earth is $3960$ miles.)

Land on a small Caribbean island is valued at $\$ 45$ per square foot. What is the value of a triangular lot with sides of lengths $80$ Ft, $50$ Ft, and $120$ Ft?

Find an angle between $0$ and $360 ^ { \circ }$ that is coterminal with each angle given a) $362 ^ { \circ }$ b) $- 870 ^ { \circ }$ c) $1170 ^ { \circ }$

Find the exact value a) $\sin \left( \frac { 19 \pi } { 2 } \right)$ b) $\cot \left( - 675 ^ { \circ } \right)$

Rewrite the expression as an algebraic expression in x. $\tan \left( \sin ^ { - 1 } x \right)$

Find the exact value of the expression. $\sin \left( \frac { \pi } { 6 } \right) \cos \left( \frac { \pi } { 3 } \right) + \sin \left( \frac { \pi } { 3 } \right) \cos \left( \frac { \pi } { 6 } \right)$

Find the values of $\sec \theta$ and $\cot \theta$ if the point $( - 3,4 )$ is on the terminal side of $\theta$ .

Find $\sec \theta$ and $\csc \theta$

The time in seconds that it takes for a sled to slide down a hillside inclined at an angle $\theta$ is $t = \sqrt { \frac { d } { 16 \sin \theta } }$ where d is the length of the slope in feet. Find the time it takes to slide down a 5000-ft slope inclined at $30 ^ { \circ }$

Find the values of $\sec \theta$ and $\cot \theta$ if the point $( - 3,4 )$ is on the terminal side of $\theta$ .

Find $\tan \theta$ and $\cot \theta$

Use Heron's formula to find the area of the triangle with sides of length 12, 18, and 24

Find the degree measure that corresponds to each radian measure. a) $- \frac { \pi } { 4 }$ b) $\frac { 11 \pi } { 4 }$

How many revolutions will a bicycle wheel of diameter $26$ inches make as the bicycle travels a distance of $4$ miles?

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. Round all answers to two decimal places. $\cos \theta = 0.9$

Find an angle between $0$ and $2 \pi$ That is coterminal with each angle given. a. $\frac { 17 \pi } { 2 }$ b. $- \frac { 15 \pi } { 4 }$ c. $85 \pi$

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. Round all answers to two decimal places. $\sin \theta = 0.7$

A pilot sets out from an airport and heads in the direction N $30 ^ { \circ }$ W, flying at a constantspeed of $305$ mi/h. Forty-five minutes later the pilot makes a course and speed correction and now heads in the direction N $50 ^ { \circ }$ W and reduces her speed to $175$ mi/h. Half an hour later, engine trouble forces her to make an emergency landing. Find the distance between the airport and the final landing point

Find the values of $\sin \theta$ and $\tan \theta$ if the point $( - 3,4 )$ is on the terminal side of $\theta$ .