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# Sin 3θ= cos(θ-26) Solve for θ

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Sin 3θ= cos(θ-26) Solve for θ

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

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
+91462
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Yes I'll go for Alan's second answer,

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

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