Trigonometric Functions Quiz

Grade 11 · Math · Quiz

Test your mastery of sine, cosine, tangent, the unit circle, identities, and graphing trig functions.

Questions

  1. What is the exact value of sin(30 degrees)?

    1. sqrt(3)/2
    2. 1/2
    3. sqrt(2)/2
    4. 1
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    Answer: 1/2

    sin(30 degrees) = 1/2 is a standard unit circle value. The 30-60-90 triangle gives sides 1, sqrt(3), 2.

  2. On the unit circle, at angle theta = 3pi/2, what are the coordinates (cos theta, sin theta)?

    1. (0, 1)
    2. (0, -1)
    3. (-1, 0)
    4. (1, 0)
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    Answer: (0, -1)

    At 3pi/2 (270 degrees), the point on the unit circle is (0, -1), so cos(3pi/2) = 0 and sin(3pi/2) = -1.

  3. The period of the function y = sin(2x) is pi, which is half the period of y = sin(x).

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    Answer: True

    The period formula is T = 2pi divided by b. For y = sin(2x), b = 2, so T = 2pi/2 = pi.

  4. Which identity is the Pythagorean Identity?

    1. sin(2 theta) = 2 sin(theta) cos(theta)
    2. sin^2(theta) + cos^2(theta) = 1
    3. tan(theta) = sin(theta) + cos(theta)
    4. cos(2 theta) = cos^2(theta) + sin^2(theta)
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    Answer: sin^2(theta) + cos^2(theta) = 1

    sin^2(theta) + cos^2(theta) = 1 is the fundamental Pythagorean Identity, derived from the unit circle equation x^2 + y^2 = 1.

  5. The amplitude of y = -3cos(x) is:

    1. -3
    2. 3
    3. 1/3
    4. 6
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    Answer: 3

    Amplitude = |a| = |-3| = 3. The negative sign reflects the graph but does not change the amplitude.

  6. tan(theta) is undefined whenever cos(theta) equals ___.

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    Answer: 0

    tan(theta) = sin(theta)/cos(theta), which is undefined when the denominator cos(theta) = 0 (at theta = pi/2, 3pi/2, etc.).

  7. Which quadrant has both sine and cosine negative?

    1. Quadrant I
    2. Quadrant II
    3. Quadrant III
    4. Quadrant IV
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    Answer: Quadrant III

    In Quadrant III, x and y are both negative, so cos(theta) < 0 and sin(theta) < 0. Only tangent is positive there.

  8. Using the double angle formula, sin(2 theta) when sin(theta) = 3/5 and theta is in Quadrant I equals:

    1. 6/25
    2. 24/25
    3. 7/25
    4. 12/25
    Show answer

    Answer: 24/25

    sin(2 theta) = 2 sin(theta) cos(theta). With sin(theta) = 3/5 and cos(theta) = 4/5 (Q1, Pythagorean), sin(2 theta) = 2 times (3/5) times (4/5) = 24/25.

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