Exam 5: Trigonometric Functions

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { a } = 59.53 \mathrm { ft } , \mathrm { c } = 223 \mathrm { ft }$ Round the missing side length to two decimal places.

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\cos 47 ^ { \circ }$

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 $\cot \theta = \frac { \sqrt { 5 } } { 6 }$

Find the exact value of the expression. - $\csc 60 ^ { \circ }$

Evaluate the expression. - $\sin ^ { 2 } 270 ^ { \circ } + \cos ^ { 2 } 270 ^ { \circ }$

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\cos \left( - 305 ^ { \circ } \right)$ and $\sin \left( - 305 ^ { \circ } \right)$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sin \left( - 33 ^ { \circ } 29 ^ { \prime } \right)$

Evaluate the expression. - $\sin 270 ^ { \circ }$

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\sin \theta = 0.31705927$

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\cos \theta = 0.1879656$

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

Find the exact value of the expression. - $\sec 1935 ^ { \circ }$

Solve the problem. -In one area, the lowest angle of elevation of the sun in winter is $21 ^ { \circ } 58 ^ { \prime }$ . A fence is to be built $13.8 \mathrm { ft }$ away from a plant in the direction of the sun. (See drawing) Find the maximum height, $x$ , for the fence so that the plant will get full sun. Round your answer to the tenths place when necessary.

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $188 ^ { \circ }$

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

Solve the problem. -Any offset between a stationary radar gun and a moving target creates a ʺcosine effectʺ that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That Is, the radar speed reading is the product of the actual reading and the cosine of the angle. Find the Radar reading to the nearest hundredth for the auto shown in the figure.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\cot 26 ^ { \circ } 26 ^ { \prime }$

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. -IV, xy

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

Find the exact value of the expression. - $\tan 300 ^ { \circ }$