Exam 6: Trigonometric Functions

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. - $\mathrm { IV } , \frac { \mathrm { r } } { \mathrm { y } }$

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. - $\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

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. - $\text { III, } \frac { \mathrm { r } } { \mathrm { x } }$

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 6 }$ and $\mathrm { c } = 12$

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\sin \theta = - \frac { 5 } { 13 }$ and $\theta$ is in quadrant III.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\cos \mathrm { A }$ when $a = 9$ and $b = 7$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { A } = 25.3 ^ { \circ } , \mathrm { b } = 3.6 \mathrm {~m}$ Round side lengths to one decimal place.

Evaluate the expression. - $\sin 90 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\cos \theta = \frac { 8 } { 17 }$ and $\theta$ is in quadrant IV.

Identify the quadrant for the angle $\theta$ satisfying the following conditions. - $\csc \theta > 0 \text { and } \sec \theta > 0$

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -A 36 -foot ladder is leaning against the side of a building. If the ladder makes an angle of $23 ^ { \circ } 45 ^ { \prime }$ with the side of the building, how far up from the ground does the ladder make contact with the building? Round your answer to the hundredths place when necessary.

Find the reference angle for the given angle. -26°

Find the exact value of the expression. - $\sec \theta$ is undefined

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is $33 ^ { \circ } 2$ '. If Joey is known to be standing 40 feet from the base of the tree, how tall is the tree (to the nearest foot)?

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { a } = 15.1 \mathrm {~cm} , \mathrm {~b} = 16.8 \mathrm {~cm}$ Round the missing side length to one decimal place.

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { A } = 11 ^ { \circ } 42 ^ { \prime } , \mathrm { c } = 201 \mathrm { ft } , \mathrm { C } = 90 ^ { \circ }$ Round side lengths to two decimal places, if necessary.

Solve the problem. -Find $\mathrm { h }$ as indicated in the figure. Round to the nearest meter.

Find the exact value of the expression. - $\cot 120 ^ { \circ }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\csc 11 ^ { \circ }$

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. - $( - 7,7 )$