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Free ACT Math: Trigonometry Questions and Answers 2 Flashcards

6 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 opposite side is 7 and the hypotenuse is 25. What is tan θ?

    Answer: 7/24

    First find adjacent side: adj = √(25² − 7²) = √(625 − 49) = √576 = 24. tan θ = opposite/adjacent = 7/24.

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

    Answer: 1/2

    From the 30-60-90 triangle: cos(60°) = adjacent/hypotenuse = 1/2. This is one of the standard values to memorize for the ACT.

  3. An angle measures 5π/6 radians. What is this in degrees?

    Answer: 150°

    Multiply by 180°/π: (5π/6) × (180/π) = 5 × 30 = 150°.

  4. If cos θ = −√3/2 and 180° < θ < 270°, what is θ?

    Answer: 210°

    cos θ = −√3/2 corresponds to reference angle 30°. In Quadrant III (180° < θ < 270°): θ = 180° + 30° = 210°.

  5. Which identity is correct?

    Answer: sin²θ + cos²θ = 1

    The Pythagorean identity sin²θ + cos²θ = 1 is fundamental in trigonometry. The related identities are: tan²θ + 1 = sec²θ and cot²θ + 1 = csc²θ.

  6. A ladder 13 feet long leans against a wall, making a 67.4° angle with the ground. How high up the wall does the ladder reach? (Use sin 67.4° ≈ 0.923)

    Answer: Approximately 12 feet

    sin 67.4° = opposite/hypotenuse = height/13. Height = 13 × 0.923 ≈ 12 feet.