Exam 5: Trigonometric Functions

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\csc \theta = - \frac { 7 } { 4 }$ and $\theta$ is in quadrant III.

Solve the problem. -On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40 meters long and the shadow is 32 meters, how tall is the flag pole?

Solve the right triangle. - $\mathrm { A } = 57 ^ { \circ } 4 ^ { \prime } , \mathrm { c } = 242 \mathrm {~m} , \mathrm { C } = 90 ^ { \circ }$ Round side lengths to two decimal places, if necessary.

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { A } = 42.2 ^ { \circ } , \mathrm { b } = 3.2 \mathrm {~m}$ Round side lengths to one decimal place.

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\csc \theta$ , given that $\sin \theta = \frac { \sqrt { 7 } } { 10 }$

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( - 20,48 ) ;$ Find $\sin \theta$ .

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\csc \theta$ , given that $\sin \theta = \frac { 1 } { 8 }$

Identify the quadrant for the angle θ satisfying the following conditions. - $\tan \theta < 0$ and $\sin \theta < 0$

Solve the problem. -A surveyor recording data for a new subdivision measured an angle as $16.82 ^ { \circ }$ . The next day, a different surveyor measured the same angle as $16 ^ { \circ } 31 ^ { \prime }$ . Find the difference between these measurements (i) to the nearest minute and (ii) to the nearest hundredth of a degree.

Identify the quadrant for the angle θ satisfying the following conditions. - $\cot \theta < 0$ and $\cos \theta > 0$

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods. - $( 5,5 )$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\csc 45 ^ { \circ }$

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\csc \theta$ , given that $\sin \theta = - 0.2305$

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $18 ^ { \circ }$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { B } = 65.4834 ^ { \circ } , \mathrm { c } = 3222.6 \mathrm {~m}$ Give side lengths to two decimal places.

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $- 302 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 10 } { 9 }$ and $\sin \theta > 0$ .

The number represents an approximate measurement. State the range represented by the measurement. - $40.07 \mathrm { k }$

Find the measure of each angle in the problem. -

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $51 ^ { \circ } 8 ^ { \prime } 26 ^ { \prime \prime }$