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Free ACT Math: Trigonometry Questions and Answers 3 Flashcards

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  1. What is the period of the function f(x) = 3 sin(2x)?

    Answer: π

    For f(x) = A sin(Bx), the period = 2π/B. Here B = 2, so period = 2π/2 = π.

  2. Which of the following is equivalent to sin(90° − θ)?

    Answer: cos θ

    This is the co-function identity: sin(90° − θ) = cos θ. Similarly, cos(90° − θ) = sin θ.

  3. In triangle ABC (not right-angled), a = 7, b = 10, and C = 45°. What is the area of the triangle?

    Answer: (1/2)(7)(10) sin 45° = 35√2/2 ≈ 24.75 sq units

    Area of a triangle = (1/2)ab sin C = (1/2)(7)(10) sin 45° = 35 × (√2/2) = 35√2/2 ≈ 24.75 square units.

  4. If tan θ = 4/3, what is sec θ in the first quadrant?

    Answer: 5/3

    Using tan θ = 4/3, we have opposite = 4, adjacent = 3, hypotenuse = √(16 + 9) = 5. cos θ = 3/5, so sec θ = 1/cos θ = 5/3.

  5. What is the amplitude of the function g(x) = −4 cos(x) + 1?

    Answer: 4

    Amplitude = |A| where A is the coefficient of the trig function. For g(x) = −4 cos(x) + 1, amplitude = |−4| = 4. The vertical shift (+1) and sign (−) do not affect amplitude.

  6. Which angle in degrees has a reference angle of 40° and lies in Quadrant IV?

    Answer: 320°

    In Quadrant IV, angles are between 270° and 360°. The reference angle is measured from the x-axis: θ = 360° − 40° = 320°.