Exam 6: Trigonometric Functions

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$ , where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). What is the grade resistance (to the nearest pound) of a 2100-lb car traveling downhill on a $5 ^ { \circ }$ grade $\left( \theta = - 5 ^ { \circ } \right)$ ?

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 $\sin \theta = \frac { 1 } { 3 }$

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

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -From a balloon 1161 feet high, the angle of depression to the ranger headquarters is $55 ^ { \circ } 2 { } ^ { \prime }$ . How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. - $\text { II, } \frac { x } { y }$

Solve the problem. -Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be $21 ^ { \circ } 32 ^ { \prime }$ . He then drives 1 mile $( 1 \mathrm { mile } = 5280 \mathrm { ft } )$ more and measures the angle of elevation to be $30 ^ { \circ } 9 ^ { \prime }$ . Find the height of the mountain to the nearest foot.

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\cot 70.5 ^ { \circ }$

Find the exact value of the expression. - $\sin 60 ^ { \circ }$

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.

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $20 ^ { \circ }$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -From a boat on the lake, the angle of elevation to the top of a cliff is $10 ^ { \circ } 11 ^ { \prime }$ . If the base of the cliff is 864 feet from the boat, how high is the cliff (to the nearest foot)?

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\csc \left( - 170 ^ { \circ } \right)$ and $\cot \left( - 170 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. -Find $\sin \theta$ , given that $\cos \theta = \frac { 2 } { 3 }$ and $\tan \theta < 0$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\cot 34 ^ { \circ } 7 ^ { \prime }$

Find the exact value of the expression. - $\cot \theta = 1$

Find the measure of each angle in the problem. -

Find the exact value of the expression. - $\sec 150 ^ { \circ }$

Evaluate the expression. - $\sec 270 ^ { \circ }$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $B = 22.1 ^ { \circ } , \mathrm { c } = 4.0 \mathrm {~mm} , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Find the angle of least positive measure coterminal with the given angle. - $565 ^ { \circ }$