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Trigonometry Flashcards

7 cards from real TMUA 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. What is the value of cos(A - B) if sin(A) = 3/5, cos(B) = 5/13, and both A and B are acute?

    Answer: 56/65

    cos A = 4/5, sin B = 12/13; cos(A-B) = cosAcosB + sinAsinB = (4/5)(5/13)+(3/5)(12/13) = 20/65+36/65 = 56/65.

  2. Which of the following is a solution to cos(2x) + cos(x) = 0 in [0, 2π]?

    Answer: x = π/3

    Substituting 2cos²x - 1 + cosx = 0 gives (2cosx - 1)(cosx + 1) = 0, so cosx = 1/2 → x = π/3.

  3. The graph of y = sin(x) is translated π/4 to the right. What is the new equation?

    Answer: y = sin(x - π/4)

    A rightward shift by c replaces x with x - c, giving y = sin(x - π/4).

  4. What is the exact value of sin(3π/4)?

    Answer: √2/2

    sin(3π/4) = sin(π - π/4) = sin(π/4) = √2/2.

  5. Which of the following identities is INCORRECT?

    Answer: sin²x + cos²x = 2

    The Pythagorean identity is sin²x + cos²x = 1, not 2; the other three identities are correct.

  6. A right triangle has hypotenuse 10 and one angle of 30°. What is the length of the side opposite the 30° angle?

    Answer: 5

    The side opposite 30° = hypotenuse × sin(30°) = 10 × 0.5 = 5.

  7. For f(x) = 2cos(x/2), what is the period?

    Answer: 4π

    The period of cos(kx) is 2π/k; with k = 1/2 the period is 2π/(1/2) = 4π.