University of Maryland Sample Exam 3 Questions
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MATH 115--SAMPLE EXAM 3 QUESTIONS
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  1. Suppose sin t = 2/5 and sec t < 0.
    1. Find the terminal point of t on the unit circle.
    2. Find the values of the following:
      1. sin (2p- t)- cos t
      2. tan (t + 3p)

    1. Locate the real number -29p/6 on the unit circle.
      2. Find two numbers, one between 0 and 2p and the other between -2p and 0, that are coterminal with -29p/6.
    2. Evaluate sin (-29p/6)

  3. Use identities, periodicity and the known values of trigonometric functions to find the value of each of the following:
    1. sin(11p/3) cot(5p/4) + cos (-23p/6)
    2. 31/2 sec2(200) - 31/2 tan2(200)
    3. cos(5p/9) cos(p/9) - sin (5p/9) sin (p/9)

  4. Evaluate each of the following. Write N.D. if the value is not defined.
    1. cot (3p/4)
    2. cos (7p/6)
    3. sec (3p/2)
    4. tan (5p/3)

  5. Let cos t = -5/7 and p < t < 3p/2. Find the exact values for each of the following:
    1. sec (-t + p/3)
    2. sin (5p/6 + t)
    3. tan t

  6. Suppose cos t = 2/7, 0 < t < p/2, sin s = 3/5, p/2 < s <p. Find the exact value of each of the following. You do not need to rationalize denominators.
    1. sin 2t
    2. cos s
    3. sin (t - s)
    4. cos (s + t )
    5. cos 2t

    1. Write the following trigonometric expression in terms of sin t and cos t, and then simplify to a single trigonometric function: sec t - (tan t)/(csc t)
    2. Draw at least one complete period of the graphs of the following functions. Your graphs should include a dotted line for each asymptote and intercepts should be labeled with their values.
      1. y = tan 2x
      2. y = sec x

  8. Write as a single trigonometric function: tan x + (cos x)/(1 + sin x)


  9. Let f(x) = 4 cos (x/3)
    1. What is the amplitude of f?
    2. What is the period of f?
    3. Graph at least two periods of f. Your graph must include the y-intercept and should have at least two x-intercepts labeled with their values. Be sure to label the axes and indicate the scale on each axis.

  10. Graph each of the following functions. Your graph should show at least two periods and the y-intercept. Be sure to label your axes and indicate the scale on each axis.
    1. f(x) = 2 sin (x + p) - 1
    2. f(x) = tan (x - p/3)

    1. Simplify the expression (1/2) (tan x + cot x) to a single trig function.
    2. Find all solutions for x (exact values in radians): 3 sin x = 2 cos2 x
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Last modified Thursday, 05-Dec-2002 11:52:15 EST           © 2008 University of Maryland