Posted by **elle** on Tuesday, July 17, 2007 at 5:39am.

hey, i would really appreciate some help solving for x when:

sin2x=cosx

Use the identity sin 2A = 2sinAcosA

so:

sin 2x = cos x

2sinxcosx - cosx = 0

cosx(2sinx - 1)=0

cosx = 0 or 2sinx=1, yielding sinx=1/2

from cosx=0 and by looking at the cosine graph, we conclude that x=pi/2 or 3pi/2 (90º and 270º)

from sinx = 1/2 and knowing that the sine is positive in the first and second quadrants, we conclude that x = pi/6 or 5pi/6 (30º and 150º)

those are the solutions in the domain 0 ≤ x ≤ 2pi,

if you want a general solution, add 2(k)pi to each of the four solutions I gave you, where k is an integer.

## Answer This Question

## Related Questions

- Trig....... - I need to prove that the following is true. Thanks (2tanx /1-tan^x...
- Trig (Last URGENT) - sin2x+cosx=0 , [-180,180) = 2sinxcosx+cosx=0 = cosx(2sinx+1...
- Precalculus/Trig - I can't seem to prove these trig identities and would really ...
- trig - express this in sinx (1/ cscx + cotx )+ (1/cscx- cotx) i got 2sinx is ...
- maths - by equating the coefficients of sin x and cos x , or otherwise, find ...
- trig - Solve for [0, 360) 2sinxcosx + cosx =0 2sinxcosx = -cosx 2sinx = -cosx/...
- Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...
- pre-calc - Solve: cos(2x-180) - sin(x-90)=0 my work: cos2xcos180 + sin2xsin180= ...
- Calc II - For the following question, we need to find the length of the polar ...
- Trigonometry - Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/...

More Related Questions