Thursday

December 18, 2014

December 18, 2014

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

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**

math (trig) - i have some problems doing trig the first one is: Show that cos(x/...

Precalculus/Trig - I can't seem to prove these trig identities and would really ...

pre-calc - Solve: cos(2x-180) - sin(x-90)=0 my work: cos2xcos180 + sin2xsin180= ...

Trig....... - I need to prove that the following is true. Thanks (2tanx /1-tan^x...

Precal - Verify the identity: sin^(1/2)x*cosx - sin^(5/2)*cosx = cos^3x sq root ...

Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...

Math - help really needed - Prove each idenity. 1+1/tan^2x=1/sin^2x 1/cosx-cosx=...

Trig (Last URGENT) - sin2x+cosx=0 , [-180,180) = 2sinxcosx+cosx=0 = cosx(2sinx+1...

Math - help really needed - I'm sorry to double post; I don't want to seem ...

trigonometry (please double check this) - Solve the following trig equations. ...