Exam 5: Trigonometric Functions

Solve the problem. -If friction is ignored, the time t (in seconds) required for a block to slide down an inclined plane is given by the formula $t = \sqrt { \frac { 2 a } { g \sin \theta \cos \theta } }$ where a is the length (in feet) of the base and g =32 feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base a = 14 when θ = 30°? If necessary, round the Answer to the nearest tenth of a second.

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

Match the given function to its graph. -1) $y = - 3 \sin \left( \frac { \pi } { 3 } x \right)$ 2) $y = - 3 \sin \left( \frac { 1 } { 3 } x \right)$ 3) $y = - 3 \cos \left( \frac { \pi } { 3 } x \right)$ 4) $y = - 3 \cos \left( \frac { 1 } { 3 } x \right)$

Write the word or phrase that best completes each statement or answers the question. -The following data represents the average percent of possible sunshine for a certain city in Indiana. Month, x Average Percent of Possible Sunshine January, 1 46 February, 2 51 March, 3 55 April, 4 60 May, 5 68 June, 6 73 July, 7 75 August, 8 74 September, 9 68 October, 10 62 November, 11 41 December, 12 38 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.

Convert the angle in radians to degrees. - $- \frac { 23 } { 9 } \pi$

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

Find the phase shift of the function. - $y = 5 \sin \left( x - \frac { \pi } { 4 } \right)$

Find the phase shift of the function. - $y = 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$

Graph the function. Show at least one period. - $y=2 \sin (2 x-\pi)$

Draw the angle. - $60 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. - $\sin \theta = \frac { \sqrt { 7 } } { 4 } , \cos \theta = \frac { 3 } { 4 } \quad$ Find $\tan \theta$ .

Solve the problem. -An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of $\frac { 1 } { 5 }$ radian is swept out, what is the linear speed of the object?

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

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. - $\left( - \frac { \sqrt { 33 } } { 7 } , - \frac { 4 } { 7 } \right)$ Find $\sin t$

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. - $\tan \left( - \frac { \pi } { 3 } \right)$

Graph the function. - $y=-2 \csc \left(x-\frac{\pi}{4}\right)$

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\sin x = 1$ ?

Find the area A. Round the answer to three decimal places. -

Graph the function. - $y = 4 \tan \left( \frac { 1 } { 2 } x \right)$

Find the exact value of the indicated trigonometric function of θ. - $\sin \theta = \frac { 1 } { 2 } , \sec \theta < 0 \quad$ Find $\cos \theta$ and $\tan \theta$