SOLUTION: find the exact value of cos(2θ)and sin(2θ) if tan(θ) = (-5/12) and 270° < θ

SOLUTION: find the exact value of cos(2θ)and sin(2θ) if tan(θ) = (-5/12) and 270° < θ < 360°

Question 1155044: find the exact value of cos(2θ)and sin(2θ) if tan(θ) = (-5/12) and 270° < θ < 360°
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

We know that  270° < θ < 360° means that θ is in quadrant IV.
We also know that the tangent is the opposite/adjacent or y/x.
So we can draw a right triangle in the 4th quadrant so that
the opposite side is the numerator +5 of the tangent (-5/12) 
taken as (+5)/(-12), and the denominator is -12 of the tangent 
taken as (+5)/(-12).  So we have the drawing: 



Next we use the Pythagorean theorem to calculate r:



Fill in the value of r=13:



Now we use the formula for sin(2θ):



and the fact that the sine is opposite/hypotenuse or y/r = (-12)/(13) = -12/13
and the fact that the cosine is adjacent/hypotenuse or x/r = (+5)/(13) = 5/13





We use the formula for cos(2θ):







 


Edwin

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