Exam 5: Trigonometric Functions

Solve the problem. -A 36-foot ladder is leaning against the side of a building. If the ladder makes an angle of $30 ^ { \circ } 53 ^ { \prime }$ 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.

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\cos 30 ^ { \circ }$

Provide an appropriate response. -Find the supplement of an angle whose measure is 37°43′15′′

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. -III, $\frac { x } { y }$

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $31 ^ { \circ } 5 ^ { \prime }$ . If the base of the cliff is 666 feet from the boat, how high is the cliff (to the nearest foot)?

Use the fundamental identities to find the value of the trigonometric function. -Find $\tan \theta$ , given that $\sec \theta = \frac { 9 } { 4 }$ and $\theta$ is in quadrant IV.

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\cos \left( 508 ^ { \circ } \right)$ and $\tan \left( 508 ^ { \circ } \right)$

Find the exact value of the expression. - $\sec \left( - 2745 ^ { \circ } \right)$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\frac { 1 } { \tan 60 ^ { \circ } 21 ^ { \prime } }$

Solve the problem. -A wheel is rotating 720 times per minute. Through how many degrees does a point on the edge of the wheel move in $\frac { 1 } { 4 }$ seconds?

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 $\theta _ { . }$ - $( - 2 , - 7 )$

Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find $\sin \mathrm { A }$ .

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

Solve the problem. -A boat sails for 4 hours at $20 \mathrm { mph }$ in a direction $106 ^ { \circ } 37$ '. How far south has it sailed (to the nearest mile)?

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 $\tan B$ when $b = 3$ and $c = 4$ .

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

Solve the problem for the given information. -What angle does the line $y = x$ make with the positive $x$ -axis?

Solve the problem. -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). A $1900 - \mathrm { lb }$ car has just rolled off a sheer vertical cliff $\left( \theta = - 90 ^ { \circ } \right)$ . What is the car's grade resistance?

Decide whether the statement is possible or impossible for an angle θ. - $\sin \theta = 6.79$