Exam 6: Trigonometric Functions

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. - $4 x + 3 y = 0 , x \geq 0 ; \quad$ Find $\cot \theta$

Find the exact value of the expression. - $\sec \left( - 2385 ^ { \circ } \right)$

Find the angle of least positive measure coterminal with the given angle. - $1313 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. -Find the exact value of x in the figure.

Solve the problem. -Find $\mathrm { h }$ as indicated in the figure. 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) - $( 3 , - 6 )$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\tan \theta = 0.25041381$

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. - $\text { IV, } \frac { x } { y }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\sec 55.3 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sin 238 ^ { \circ } 19 ^ { \prime }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 4 } { 7 }$ and $\sin \theta > 0$ .

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 $\theta$ - $( - 20,48 ) ;$ Find $\sin \theta$

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 $I$ and the positive $x$ -axis is $\frac { \sqrt { 2 } } { 2 }$ .

Use the fundamental identities to find the value of the trigonometric function. -Find $\sec \theta$ , given that $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant I.

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $77 ^ { \circ } 39 ^ { \prime }$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\tan 60 ^ { \circ }$

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. - $( - 8 , - 8 )$

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) - $( - 2 , - 7 )$

Solve the problem. -A wheel makes 282 revolutions per minute. How many revolutions does it make per second?

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\cos \theta = \frac { 2 } { 11 } \text { and } \sec \theta = \frac { 11 } { 2 }$