Asia M.

asked • 11/28/16

Exact Value 12.

if cosθ= -3/5 and θ is in quadratic 2, using the double angle formulas, find the exact value of each expression
 
(a) cos (2θ)
 
(b) sin (2θ)
 
Show details in answer please.

1 Expert Answer

By:

Michael J. answered • 11/28/16

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Effective High School STEM Tutor & CUNY Math Peer Leader

Asia M.

Hello,
You answered the question 3/4 of the way. Not completely. So would I substitute x for 4/5? For example, for (a) would it be sin(2(4/5))=1-2sin(4/5)? And if so would it simplify to sin(8/5)=1-2sin2 (4/5)? Like what would be the final solution for (a)? Same question and methodology for (b). What would be the final answer for (b)?
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11/30/16

Michael J.

I think you missed the last statement when I said plug in the values of sinx and cosx into the identities.  I will do the first one for you so you know how it is done.
 
cos(2x) = 1 - 2sin2x
           = 1 - 2(16/25)
 
Simplify.
 
 
Now try the other one.
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11/30/16

Asia M.

So,  for cos (2θ)= (-7/25). Now you have to use the equation sin(2x)=2sinxcosx and plug in both sinx and cosx to get (b) I believe. I would go about that by doing this: 2(4/5)(-7/25). Then you get -56/125 for sin(2θ). Am I Right?
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11/30/16

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