Exam 6: Trigonometric Functions

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. - $\tan \theta$ , given that $\cot \theta = - \frac { 2 } { 3 }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sec 55 ^ { \circ } 28 ^ { \prime }$

Find the exact value of the expression. - $\csc 240 ^ { \circ }$

Evaluate the expression. - $\cot ^ { 2 } 90 ^ { \circ } - \sec 180 ^ { \circ }$

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

Perform the calculation. - $90 ^ { \circ } - 38 ^ { \circ } 24 ^ { \prime } 40 ^ { \prime \prime }$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { B } = 65.4834 ^ { \circ } , \mathrm { c } = 3851.3 \mathrm {~m}$ Give side lengths to two decimal places.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -A formula used by an engineer to determine the safe radius of a curve, $R$ , when designing a road is: $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$ , where $\alpha$ is the superelevation of the road and $\mathrm { V }$ is the velocity (in feet per second) for which the curve is designed. If $\mathrm { V } = 72 \mathrm { ft }$ per sec, $\mathrm { f } = 0.1 , \mathrm {~g} = 30$ , and $\alpha = 1.8 ^ { \circ }$ , find $\mathrm { R }$ . Round to the nearest foot.

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the given point is on the terminal side of $\theta$ (3, 6) - $( - 5 , - 3 )$

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the given point is on the terminal side of $\theta$ (3, 6) - $( - 5,3 )$

Solve the problem. -A boat sails for 4 hours at $20 \mathrm { mph }$ in a direction $125 ^ { \circ } 32 ^ { \prime }$ . How far south has it sailed (to the nearest mile)?

Find the exact value of the expression. - $\tan 510 ^ { \circ }$

Find the exact value of the expression. - $\sin \left( - 960 ^ { \circ } \right)$

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

Find the measure of each angle in the problem. -Supplementary angles with measures $3 x + 2$ and $2 x + 3$ degrees

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\sec \left( 704 ^ { \circ } \right)$ and $\sin \left( 704 ^ { \circ } \right)$

An equation of the terminal side of an angle $\theta$ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of $\theta$ . Do not use a calculator. - $y = 3 x , x \geq 0 ; \quad$ Find $\tan \theta$