Unit 5 PreCalculus Review

Transcription

1 Class: Date: Unit 5 PreCalculus Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the terminal point P (x, y) on the unit circle determined by t = π. Round the values to the nearest 4 hundredth. a. (0.1, 0.1) b. ( 0.1, 0.1) c. (0.8, 0.85) d. ( 0.1, 0.1) 2. Find the terminal point P (x, y) on the unit circle determined by t = 5π hundredth. a. (0.8, 0.50) b. ( 0.99, 0.4) c. ( 0.8, 0.50) d. ( 0.8, 0.50). Round each value to the nearest. Find the terminal point P (x, y) and the reference number determined by t = 19π. Round the coordinates of the terminal point to the nearest hundredth, and express the reference number in terms of π a. terminal point is ( 0.8, 0.50), reference number is π b. terminal point is ( 0.8, 0.50), reference number is 5π c. terminal point is (0.8, 0.50), reference number is π d. terminal point is ( 0.8, 0.50), reference number is π 1

2 4. Use the figure to find the terminal point determined by the real number t = Round the values to one decimal place. a. terminal point is ( 0., 0.8) b. terminal point is ( 0.8, 0.) c. terminal point is (0., 0.8) d. terminal point is (0.8, 0.) 5. Find the exact values of the trigonometric functions sec 1 π and csc π. a. sec 1 π =, csc π = b. sec 1 π =, cot π = 2 c. sec 1 π = 2, csc π = 2. The terminal point determined by t is Ê ˆ 4, Find sin t, cos t, and tan t. 4. a. sint = 4, cost = 4, tant = b. sint = c. sint = 4, cost = 4, tant = 4, cost = 4, tant = 2

3 . Find the values of the trigonometric functions of t if sint = 1 and sec t < 0. a. sint = 1, cost = 1, tant = 1, cot t = 1 1 b. sint = 1, cost =, tant = 1, cot t = 1 1 c. sint = 1, cost =, tant = 1, cot t = 1 1 Short Answer 1. Find the terminal point P(x,y) on the unit circle determined by the given value of t = 5π. 2. Find the approximate value of the given trigonometric function. tan( 4.) (a) By using the figure. Please give the answer to one decimal place. tan( 4.) = (b) By using a calculator in radians. Please give the answer to five decimal places. tan( 4.) =

4 . As a wave passes by an offshore piling, the height of the water is modeled by the function Ê h(t) = cos π 1 t ˆ where h(t) is the height in feet above mean sea level at time t seconds. (a) Find the period of the wave. period = seconds (b) Find the wave height, that is, the vertical distance between the trough and the crest of the wave. wave height = feet 4. The carrier wave for an FM radio signal is modeled by the function Ê y = a sin 2π Ê ˆ ˆ t where t is measured in seconds. (a) Find the period of the carrier wave. Round the expression that precedes the multiplication sign to two decimal places. 10 s (b) Find the frequency of the carrier wave. Round the expression that precedes the multiplication sign to two decimal places. 10 Hz Ê ˆ 4 5. Suppose that the terminal point determined by t is, Find the terminal point determined by t + π.. 4

5 . When a car hits a certain bump on the road, a shock absorber on the car is compressed a distance of in., then released. The shock absorber vibrates in damped harmonic motion with a frequency of 2 cycles per second. The damping constant for this particular shock absorber is 2.. Find an equation that describes the displacement of the shock absorber from its rest position as a function of time. Take t = 0 to be the instant that the shock absorber is released.. Each time your heart beats, your blood pressure increases, then decreases as the heart rests between beats. A certain person's blood pressure is modeled by the function p(t) = sin(10πt) where p(t) is the pressure in mmhg at time t, measured in minutes. Find the amplitude, period, and frequency of p. 8. Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t = 0. amplitude 28 cm, period 8 s 9. Find the period and graph the function. y = sec x 10. Find the period and graph the function. y = 1 5 csc x 11. Sketch the graph. y = 15sin 1 2 x 5

6 12. The point P is on the unit circle. The x-coordinate of P is 1 and P is in quadrant I. Find the point P(x, y). 1. Find the exact values of the trigonometric functions sin π and sin 1 π. 14. Find the exact values of the trigonometric functions sec 9π and csc 1 2 π.

7 Unit 5 PreCalculus Review Answer Section MULTIPLE CHOICE 1. ANS: A 2. ANS: D. ANS: A 4. ANS: D 5. ANS: C. ANS: B. ANS: B SHORT ANSWER 1. ANS: Ê 1 2, 2 ˆ 2. ANS: 2.; ANS: 2; 4. ANS: 1.04, -8; 9.5, 5. ANS: Ê 4, ˆ. ANS: f(t) = e 2.t cos 4πt 1

8 . ANS: Amplitude 20, period , frequency ANS: f(t) = 28cos π 4 t 9. ANS: period 2π 10. ANS: period 2π 2

9 11. ANS: 12. ANS: Ê ˆ 1, ANS: sin π = 0.5, sin 1 π = ANS: sec 9π = 1, csc 1 2 π = 1