Posted by **george** on Tuesday, January 1, 2013 at 1:23pm.

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

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

- trigonometry -
**Reiny**, Tuesday, January 1, 2013 at 2:36pm
14.

sin 2x + sinx = 0

2sinxcosx + sinx = 0

sinx(2cosx + 1) = 0

sinx = 0 or sinx = -1/2

for sinx = 0

**x = 0, π, 2π**

for sinx = -1/2

**x = 7π/6 or 11π/6** ( 210° or 330°)

21.

recall:

cos u - cosv = -2sin( (u+v)/2 ) sin( (u-v)/2 )

let (u+v)/2 = 37 ---> u+v = 74

let (u-v)/2= 26 ----> u-v = 52

add them:

2u = 126

u = 63 , then v = 11

-2 sin((63+11)/2) sin((63-11)/2) = cos 63 - cos 11

2 sin((63+11)/2) sin((63-11)/2) = cos11° - cos63°

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