Trigonometric Double Angle Formulas

stevo_evo_22

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Jul 22, 2008
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Hi everyone!

Here is the question I am stuck on:

Find the value of theta and state any restrictions on the value of theta: {theta:cos2theta=cos^2theta}, 0_<_theta_<_2pi.

(Sorry if you can't understand the question, i'm not used to using math tags:))

I have solved for costheta and worked it out to be 1 (or at least I think) but when it come to giving the value of theta, i only get 0 and 2pi. The book's answer also includes 3pi/2. Where have I gone wrong?

Thanks in advance,
Steven
 
You ignored cos(θ)=1\displaystyle \cos(\theta) = - 1.
 
Hello, Steven!

Roy is absolutely correct . . .


Find the value of θ\displaystyle \theta and state any restrictions on θ\displaystyle \theta

. . \(\displaystyle \cos2\theta \:=\:\cos^2\!\theta},\qquad 0\,\leq \,\theta \,<\,2\pi\)

Use the identity: cos2θ=2cos2 ⁣θ1\displaystyle \text{Use the identity: }\:\cos2\theta \:=\:2\cos^2\!\theta - 1

The equation becomes: 2cos2 ⁣θ1=cos2 ⁣θcos2 ⁣θ=1cosθ=±1\displaystyle \text{The equation becomes: }\:2\cos^2\!\theta - 1 \:=\:\cos^2\!\theta \quad\Rightarrow\quad \cos^2\!\theta \:=\:1 \quad\Rightarrow\quad \cos\theta \:=\:\pm1


. . Then: cosθ=1θ=0\displaystyle \text{Then: }\:\cos\theta\:=\:1 \quad\Rightarrow\quad \theta \:=\:0

. . And: cosθ=-1θ=π\displaystyle \text{And: }\:\cos\theta \:=\:\text{-}1 \quad\Rightarrow\quad \theta \:=\: \pi


Edit: corrected my (really stupid) errors.
Thanks for pointing them out, masters!
.
 
Of course! Thankyou to both of you! I will remember next time about square-rooting cosine! Thanks!!!! :D
 
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