# Solve the equation??

• Mar 28th 2009, 06:39 AM
Viky
Solve the equation??
If -180o <= 180o , solve the equation

cos(2theta - 70o) = sin(theta+40o)
• Mar 28th 2009, 10:25 AM
stapel
Quote:

Originally Posted by Viky
If -180o <= 180o , solve the equation

cos(2theta - 70o) = sin(theta+40o)

A good start would probably to apply sum and difference identities, so you can get $\displaystyle \sin(\theta)$ and $\displaystyle \cos(\theta)$ by themselves, and then work from there.

. . . . .$\displaystyle \cos(2\theta\, -\, 70^{\circ})\, =\, \cos(2\theta)\cos(70^{\circ})\, +\, \sin(2\theta)\sin(70^{\circ})$

. . . . .$\displaystyle \sin(\theta\, +\, 40^{\circ})\, =\, \sin(\theta)\cos(40^{\circ})\, +\, \cos(\theta)\sin(40^{\circ})$

And note also the double-angle identities:

. . . . .$\displaystyle \cos(2\theta)\, =\, \cos^2(\theta)\, -\, \sin^2(\theta)$

. . . . .$\displaystyle \sin(2\theta)\, =\, 2\sin(\theta)\cos(\theta)$

If you get stuck please reply showing your steps and how far you have gotten. Thank you! :D
• Mar 30th 2009, 07:32 AM
Viky
thanks
how do i insert the theta symbol?
• Jul 20th 2009, 08:00 PM
mr fantastic
Quote:

Originally Posted by Viky
how do i insert the theta symbol?

Type $$\theta$$.

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