Trig functions unit test review

Which values for theta have the same reference angles? a. pi/6, pi/3, 5pi/6 b. pi/3, 5pi/6, 4pi/3 c. pi/2, 5pi/4, 7pi/4 d. pi/4, 3pi/4, 7pi/4

D. pi/4, 3pi/4, 7pi/4

A student is given that point P(a, b) lies on the terminal ray of angle theta, which is between 3pi/2 radians and 2pi radians. The student uses the steps below to find cos theta. (table shown with 3 steps). Which of the following explains whether the student is correct? a. The student made an error in step 3 because a is positive in Quadrant IV; therefore, b. The student made an error in step 3 because . c. The student made an error in step 2 because r is negative in Quadrant IV; therefore, . d. The student made an error in step 2 because using the Pythagorean theorem gives .

a. The student made an error in step 3 because a is positive in Quadrant IV; therefore,

Which statement accurately describes how adding a number, n, to the function f(x)=sin(x) affects its graph? a. There is a vertical shift of n units. b. The x-intercepts will shift n units. c. There is a change in amplitude of n units. d. The range will change by a factor of 2n units.

a. There is a vertical shift of n units.

What is the approximate length of arc s on the circle below? Use 3.14 for pi. Round your answer to the nearest tenth. a. 5.8 ft b. 6.3 ft c. 27.5 ft d. 69.1 ft

d. 69.1 ft

Which of the following represents the measures of all angles conterminal with a -220° angle? a. 360 + 140n, for any whole number n b. 360 + 140n, for any integer n c. 140 + 360n, for any whole number n d. 140 + 360n, for any integer n

d. 140 + 360n, for any integer n

Angle B has a measure between 0° and 360° and is coterminal with a -865° angle. What is the measure of angle B? a. 110° b. 115° c. 210° d. 215°

d. 215°

Which of the following are in correct order from greatest to least? a. pi/2, 330, 5pi/3, 7pi/6, 2pi/3 b. 5pi/3, 7pi/6, 2pi/3, pi/2, 330 c. pi/2, 2pi/3, 7pi/6, 5pi/3, 330 d. 330, 5pi/3, 7pi/6, 2pi/3, pi/2

d. 330, 5pi/3, 7pi/6, 2pi/3, pi/2

The graph of which function passes through (0,3) and has an amplitude of 3? a. f(x)=sin(x)+3 b. f(x)=cos(x)+3 c. f(x)=3sin(x) d. f(x)=3cos(x)

d. f(x)=3cos(x)

Henry is asked to find the exact value of cos(10pi/3). His steps are shown below. 1. Subtract 2pi from 10pi/3 as many times as possible: 10pi/3 - 2pi = 4pi/3 2. Find the reference angle for 4pi/3 : 3pi/2 - 4pi/3 = pi/6 3. The cosine value for pi/6 is sqrt 3/2 4. The cosine value is positive because pi/6 is in the first quadrant. Which of the following describes Henry's errors? a. The reference angle should be pi/3, and the sign of the value should be negative. b. The reference angle should be pi/3, and the cosine value for pi/3 is 1/2 c. The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting pi in the first step. d. The cosine value for pi/6 is 1/2, and the reference angle and quadrant should be determined by subtracting pi in the first step.

a. The reference angle should be pi/3, and the sign of the value should be negative.

If a vertical line is dropped from the x-axis to the point (12, -9) in the diagram below, what is the value of sec theta? a. -5/3 b. -5/4 c. 5/4 d. 5/3

c. 5/4

An angle in standard position measures pi/2 radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle? a. -1 b. 0 c. 1 d. undefined

b. 0

Which measure is of an angle that is coterminal with a 95° angle? a. 95° - (1,450n)°, for any integer n b. 95° - (1,080n)°, for any integer n c. 95° - (780n)°, for any integer n d. 95° - (340n)°, for any integer n

b. 95° - (1,080n)°, for any integer n

Which function is the same as y= 3cos(2(x+ pi/2)) -2? a. y= 3sin (2(x+ pi/4)) -2 b. y= -3sin (2(x+ pi/4)) -2 c. y= 3cos(2(x+ pi/4)) -2 d. y= -3cos (2(x+ pi/2)) -2

b. y= -3sin (2(x+ pi/4)) -2

An angle that shares the same sine value of an angle that measures 5pi/4 radians is located where? a. Quadrant I b. Quadrant II c. Quadrant IV d. along an axis

c. Quadrant IV

Which of the following is true for f(x) = -2sin(x) - 3? a. The range of the function is the set of real numbers -2 <= y <= 2 b. The graph of the function is the graph of f(x) = -2sin(x) shifted 3 units up. c. The amplitude of the function is 2. d. The period of the function is 4pi.

c. The amplitude of the function is 2.