Exam 5: Trigonometric Functions

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\tan \left( - 30 ^ { \circ } \right)$

Solve the problem. -A racetrack curve is banked so that the outside of the curve is slightly elevated or inclined above the inside of the curve. This inclination is called the elevation of the track. The maximum speed on the track in miles per Hour is given by $\sqrt { r ( 29000 + 41000 \tan \theta ) }$ where r is the radius of the track in miles and θ is the elevation in degrees. Find the maximum speed for a Racetrack with an elevation of 26° and a radius of 0.6 miles. Round to the nearest mile per hour.

Write the word or phrase that best completes each statement or answers the question. - $\text { If } f ( \theta ) = \sin \theta \text { and } f ( a ) = - \frac { 1 } { 9 } , \text { find the exact value of } f ( a ) + f ( a - 4 \pi ) + f ( a - 2 \pi )$

Match the function to its graph. - $y = - \tan ( x + \pi )$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = 15.3$ centimeters, $\theta = 3.5$ radians, $\mathrm { s } =$ ?

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. -5

Find an equation for the graph. -

Write the word or phrase that best completes each statement or answers the question. -Before exercising, an athlete measures her air flow and obtains $a = 0.65 \sin \left( \frac { 2 \pi } { 5 } t \right)$ where a is measured in liters per second and t is the time in seconds. If a > 0, the athlete is inhaling; if a < 0, the athlete is exhaling. The time to complete one complete inhalation/exhalation sequence is a respiratory cycle. What is the amplitude? What is the period? What is the respiratory cycle? Graph a over two periods beginning at t = 0.

Find the length s. Round the answer to three decimal places. -

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 9 ^ { \circ }$

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\sin ^ { 2 } 80 ^ { \circ } + \cos ^ { 2 } 80 ^ { \circ }$

Convert the angle to a decimal in degrees. Round the answer to two decimal places. -23°47'37"

Find the exact value. Do not use a calculator. - $\cos \frac { \pi } { 2 }$

Convert the angle in radians to degrees. - $\frac { \pi } { 6 }$

Name the quadrant in which the angle θ lies. - $\cos \theta > 0 , \quad \csc \theta < 0$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( - \frac { \sqrt { 55 } } { 8 } , \frac { 3 } { 8 } \right) \quad$ Find $\cot t$

Write the word or phrase that best completes each statement or answers the question. -The following data represents the normal monthly precipitation for a certain city in Arkansas. Month, x Normal Monthly Precipitation, inches January, 1 3.91 February, 2 4.36 March, 3 5.31 April, 4 6.21 May, 5 7.02 June, 6 7.84 July, 7 8.19 August, 8 8.06 September, 9 7.41 October, 10 6.30 November, 11 5.21 December, 12 4.28 Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form y = A sin (ωx - Φ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Choose the one alternative that best completes the statement or answers the question. -In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of 2.4 x 104 miles. The orbit is circular, and one revolution around Earth takes 10.1 days. Assuming the radius of the Earth is 3960 Miles, find the linear speed of the satellite. Express the answer in miles per hour to the nearest whole mile.

Find the exact value. Do not use a calculator. - $\tan 2 \pi$

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad$ Find $f ( \theta )$