Homework Help: maths

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.

No one has answered this question yet.

Answer this Question

Related Questions

math (trig) - i have some problems doing trig the first one is: Show that cos(x/...
Math - help really needed - Prove each idenity. 1+1/tan^2x=1/sin^2x 1/cosx-cosx=...
TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
Math - help really needed - I'm sorry to double post; I don't want to ...
pre-calc - Solve: cos(2x-180) - sin(x-90)=0 my work: cos2xcos180 + sin2xsin180= ...
trig - I need to prove equality. a) (sina + cosa)^2 -1 / ctga - sinacosa = 2tg^...
algebra - Can someone please help me do this problem? That would be great! ...
Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...
Math - Calculus - The identity below is significant because it relates 3 ...
trig - express this in sinx (1/ cscx + cotx )+ (1/cscx- cotx) i got 2sinx is ...

For Further Reading

First Name:
School Subject:
Answer: