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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 side opposite a 30° angle has length 5. What is the length of the hypotenuse?

    Answer: 10

    sin(30°) = opposite/hypotenuse = 1/2, so hypotenuse = 5 / (1/2) = 10.

  2. What is the exact value of cos(60°)?

    Answer: 1/2

    cos(60°) is a standard value equal to 1/2.

  3. If tan(θ) = 3/4 and θ is acute, what is sin(θ)?

    Answer: 3/5

    With opposite 3 and adjacent 4, the hypotenuse is 5, so sin(θ) = 3/5.

  4. Which identity is always true for any angle θ?

    Answer: sin²θ + cos²θ = 1

    The Pythagorean identity sin²θ + cos²θ = 1 holds for all angles.

  5. A ladder leans against a wall making a 70° angle with the ground. If the ladder is 12 ft long, how high up the wall does it reach (nearest tenth)?

    Answer: 11.3 ft

    Height = 12 · sin(70°) ≈ 12 · 0.9397 ≈ 11.3 ft.

  6. What is the period of the function y = sin(x)?

    Answer: 2π

    The sine function repeats every 2π radians.

  7. Convert 180° to radians.

    Answer: π

    Since 180° equals half a circle, it equals π radians.