Exam 6: An Introduction to Trigonometry Via Right Triangles

Use the following information to determine the remaining five trigonometric values. Rationalize any denominators that contain radicals. $\cos \theta = - \frac { 4 } { 7 } , 90 ^ { \circ } < \theta < 180 ^ { \circ }$

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the angle. $- 720 ^ { \circ }$

Find the area of the triangle. Use a calculator and round your final answer to two decimal places.

Evaluate the expression using the concept of a reference angle. $\cos \left( - 675 ^ { \circ } \right)$

Use the definitions to evaluate the six trigonometric functions of $\theta$ . In cases in which a radical occurs in a denominator, rationalize the denominator.

Use the following information to express the remaining five trigonometric values as functions of $t$ . Assume that $t$ is positive. Rationalize any denominators that contain radicals. $\cos \theta = - \frac { 3 t } { 4 } , 90 ^ { \circ } < \theta < 180 ^ { \circ }$

From a point on ground level, you measure the angle of elevation to the top of a mountain to be $37 ^ { \circ }$ . Then you walk $150 \mathrm {~m}$ farther away from the mountain and find that the angle of elevation is now $20 ^ { \circ }$ . Find the height of the mountain.

Use the following formation to determine the remaining five trigonometric values. Rationalize any denominators that contain radicals. $\sec B = - \frac { 9 } { 4 } , 180 ^ { \circ } < B < 270 ^ { \circ }$

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the angle. $900 ^ { \circ }$

The accompanying figure shows two ships at points $P$ and $Q$ , which are in the same vertical plane as an airplane at point $R$ . When the height of the airplane is $3,100 \mathrm { ft }$ , the angle of depression to $P$ is $35 ^ { \circ }$ and that to $Q$ is $30 ^ { \circ }$ .Find the distance between the two ships.

Determine the answer that establishes an identity. $\frac { \sin \theta } { \csc \theta } + \frac { \cos \theta } { \sec \theta } = ?$

In $\triangle A C D$ , you are given $\angle C = 90 ^ { \circ } , \angle A = 60 ^ { \circ }$ and $A C = 9$ . If $B$ is a point on $\overline { C D }$ and $\angle B A C = 45 ^ { \circ }$ , find $B D$ .

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the angle. $- 900 ^ { \circ }$

Determine the answer that establishes an identity. $\csc ^ { 2 } A + \sec ^ { 2 } A = ?$

Determine the answer that establishes an identity. $\frac { \sin B } { 1 + \cos B } + \frac { 1 + \cos B } { \sin B } = ?$

Refer to the figure. If $\angle A = 60 ^ { \circ }$ and $A B = 40 \mathrm {~cm}$ , find $A C$ .

Suppose that $\triangle A B C$ is a right triangle with $\angle C = 90 ^ { \circ }$ . If $A B = 3$ and $B C = \frac { 3 \sqrt { 3 } } { 2 }$ , find the quantities. $\cos A , \sin B$

The radius of the circle in the figure is 2 units. Express the length $D C$ in terms of $\alpha$ .

Evaluate the expression using the concept of a reference angle. $\sin \left( - 150 ^ { \circ } \right)$

Use the following information to express the remaining five trigonometric values as functions of $u$ . Assume that $u$ is positive. Rationalize any denominators that contain radicals. $\cos \theta = \frac { u } { \sqrt { 10 } } , 0 ^ { \circ } < \theta < 90 ^ { \circ }$