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*girlie*
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Find, in degrees, the value of Theta in the interval of 0<=Theta<360 for which:

2cos^2Theta – cosTheta – 1 = Sin^2Theta

Could somebody please work this out for me and show ALL their working, because I have NO idea how to do these sort of questions.
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yazan_l
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2cos²@ – [email protected] – 1 = Sin²@

now sin²@ = 1- cos²@

2cos²@ – [email protected] – 1 = 1 - cos²@
3 cos²@ - [email protected] - 2 = 0
([email protected] + 2) ([email protected] - 1) = 0
[email protected] = -2/3 or [email protected] = 1
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damaster275
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(Original post by *girlie*)
Find, in degrees, the value of Theta in the interval of 0<=Theta<360 for which:

2cos^2Theta – cosTheta – 1 = Sin^2Theta

Could somebody please work this out for me and show ALL their working, because I have NO idea how to do these sort of questions.
Well, first you have to use the trig identity sin^2theta + cos^2theta = 1
Which can be rearranged to give sin^2theta = 1 - cos^2theta
Substitution gives:
2 cos^2tgheta - costheta - 1 = 1 - cos^2theta
=> 3 cos^2theta - costheta -2 = 0
=> (3costheta + 2)(costheta - 1)=0
so, 3 costheta = -2, and costheta = 1
then solve for theta (Can't be bothered to do it)
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