Question

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).

Answer 1

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.