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trigonometry

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5. If cot 2θ = 5/12 with 0 ≤ 2θ ≤ π , find cosθ, sinθ, and tanθ

8. Find the exact value of sin2a if cosa = 4/5(a in Quadrant I)

13. Find the exact value of tan2 if sinB = 5/13 (B in quadrant II)

14. Solve sin 2x + sin x = 0 for 0 ≤ x ≤ 2π.

21. Write 2sin37°sin26° as a sum (or difference).

  • trigonometry -

    5.
    since cot(x) < 0 in QII, 2θ is in QI
    so, we have a 5-12-13 triangle in QI.

    8.
    we have a 3-4-5 triangle, so sina = 3/5

    13.
    again, a 5-12-13 in QII, so y>0 and x<0

    14.
    review sum-to-product formulas:

    sin u + sin v = 2 sin(½(u+v)) cos(½(u−v))

    21. review product-to-sum formulas:

    sin A sin B = ½ cos(A−B) − ½ cos(A+B)

    If you get stuck, or want to check your answers come on back.

    If stuck, where do you run aground? Remember to draw the triangles where involved, paying attention to quadrants.

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