Exam 6: Trigonometric Functions

Solve the problem. -A fire is sighted due west of lookout $\mathrm { A }$ . The bearing of the fire from lookout $\mathrm { B } , 13.8$ miles due south of A, is $\mathrm { N } 44 ^ { \circ } 15 ^ { \prime } \mathrm { W }$ . How far is the fire from B (to the nearest tenth of a mile)?

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $161 ^ { \circ } 53 ^ { \prime } 19 ^ { \prime \prime }$

Evaluate the expression. - $6 \tan 180 ^ { \circ } + 5 \csc 270 ^ { \circ }$

Evaluate the expression. - $\tan \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { A } = 11 ^ { \circ } 14 ^ { \prime } , \mathrm { c } = 247 \mathrm { ft }$ Round side lengths to two decimal places.

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

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $- 210 ^ { \circ }$

Convert the angle to degrees, minutes, and seconds. - $10.66 ^ { \circ }$

Perform the calculation. - $94 ^ { \circ } 22 ^ { \prime } - 27 ^ { \circ } 36 ^ { \prime }$

Evaluate the expression. - $\cos \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\sin \theta = 0.7 \text { and } \csc \theta = - 0.7$

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

Find the measure of each angle in the problem. -

Evaluate the expression. - $\cot \left( - 90 ^ { \circ } \right)$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $22 ^ { \circ } 9 ^ { \prime }$ . If the dam is 1421 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Find the angle of least positive measure coterminal with the given angle. - $- 295 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sin \left( - 48 ^ { \circ } 49 ^ { \prime } \right)$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ - $( 18,24 ) ;$ Find $\csc \theta$

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $\mathrm { I }$ and the positive $\mathrm { x }$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

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 $3000 - \mathrm { lb }$ car traveling uphill on a $3 ^ { \circ }$ grade $\left( \theta = 3 ^ { \circ } \right)$ ?