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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. An airplane climbs at a constant 15° angle. After traveling 2000 ft along its path, how high is it (nearest foot)?

    Answer: 518 ft

    Altitude = 2000 · sin(15°) ≈ 2000 · 0.2588 ≈ 518 ft.

  2. What is the exact value of cos(90°)?

    Answer: 0

    The cosine of 90° is 0.

  3. Simplify the expression sin(θ)/cos(θ).

    Answer: tan(θ)

    By definition, sin(θ)/cos(θ) equals tan(θ).

  4. The graph of y = sin(x) is shifted to become y = sin(x − π/2). This is equivalent to which function?

    Answer: -cos(x)

    Shifting sine right by π/2 produces −cos(x).

  5. In which quadrant is sine positive but cosine negative?

    Answer: Quadrant II

    In Quadrant II, y is positive (sine +) and x is negative (cosine −).

  6. If a right triangle has legs of 9 and 12, what is the measure of the smallest angle (nearest degree)?

    Answer: 37°

    The smallest angle is opposite the shorter leg: arctan(9/12) ≈ 37°.

  7. What is the value of tan(0°)?

    Answer: 0

    Since sin(0°) = 0 and cos(0°) = 1, tan(0°) = 0/1 = 0.