Exam 6: Trigonometric Functions: Right Triangle Approach

Find the reference angle for $\theta = \frac { 22 } { 7 }$ .

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

Solve the triangle. $a = 72.5 , \quad \angle B = 60 ^ { \circ } , \quad \angle C = 82 ^ { \circ }$

Use the Law of Sines to find $x$ .

Find the area of the triangle.

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

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 exact value of each expression, if it is defined. (a) $\cos ^ { - 1 } ( - \sqrt { 2 } / 2 )$ (b) $\sin ^ { - 1 } ( - \sqrt { 2 } / 2 )$ (c) $\tan ^ { - 1 } ( - \sqrt { 3 } )$

A 18-ft ladder leans against a building so that the angle between the ground and the ladder is $72 ^ { \circ }$ . How high does the ladder reach on the building?

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

Find the reference angle for $\theta = - 39 ^ { \circ }$

Find the quadrant in which $\theta$ lies given that $\cot \theta > 0$ and $\sin \theta < 0$ .

Find the length of an arc of a circle of radius $12$ ft if the arc subtends a central angle of $135 ^ { \circ }$ .

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

Find the reference angle for $\theta = \frac { 19 \pi } { 6 }$ .

Use the Law of Sines to solve for all possible triangles that satisfy $a = 9$ , $b = 13$ , $\angle B = 67 ^ { \circ }$ .

Use the Law of Cosines to find $x$ .

A plane leaves the airport at 4:00 p.m. and heads in the direction N $10 ^ { \circ }$ E at a constant speed of $250$ mi/h. Forty-five minutes later, a jet leaves the same airport and flies N $60 ^ { \circ }$ W at a constant speed of $450$ mi/h. Find the distance between the plane and the jet at 5:30 p.m.

Solve the triangle using the Law of Sines.

Find the exact value of $\csc ( - 23 \pi / 4 )$ .