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Math: Trigonometry Flashcards

7 cards from real ACT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. In a right triangle, the two legs measure 6 and 8. What is sin of the angle opposite the leg of length 6?

    Answer: 6/10

    The hypotenuse is 10, so sine of that angle is opposite/hypotenuse = 6/10.

  2. What is the exact value of tan(45°)?

    Answer: 1

    In a 45-45-90 triangle the legs are equal, so tan(45°) = 1.

  3. Using the law of sines, if a = 10, sin A = 0.5, and sin B = 0.8, what is side b?

    Answer: 16

    b = a · sin B / sin A = 10 · 0.8 / 0.5 = 16.

  4. What is the amplitude of y = 3sin(2x)?

    Answer: 3

    The amplitude is the coefficient in front of sine, which is 3.

  5. Which expression equals sec(θ)?

    Answer: 1/cosθ

    Secant is the reciprocal of cosine, so sec(θ) = 1/cos(θ).

  6. A right triangle has a hypotenuse of 13 and one leg of 5. What is cos of the angle adjacent to the leg of length 5?

    Answer: 5/13

    Cosine is adjacent/hypotenuse = 5/13 for the angle adjacent to that leg.

  7. Convert π/4 radians to degrees.

    Answer: 45°

    Multiply π/4 by 180/π to get 45°.