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Sin 3θ= cos(θ-26) Solve for θ

math
Guest Aug 20, 2014
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 #1
avatar+26322 
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I think you will need to solve this numerically.  The graphs below might help:

trig. curves

The first two solutions above are at θ = 29° and 32°

 

On second thoughts, a numerical solution might be overkill!  If θ - 26° is in the first quadrant, then cos(θ - 26°) = sin(90°- θ + 26°).  In this case 3θ = 116° - θ or 4θ = 116° or θ = 29°.

Alan  Aug 20, 2014
 #2
avatar+90988 
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Yes I'll go for Alan's second answer,

 

Consider this triangle,         $$sin\theta = \frac{o}{hyp} = cos(90-\theta)$$

 

so in your question

$$\\sin3\theta = cos(90-3\theta)=cos(\theta-26)\\
therefore\\
90-3\theta=\theta-26\\
116=4\theta\\
\theta=29^0$$

Melody  Aug 21, 2014

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