Question 829513: Find the exact value of cos(arctan11/60)
At first, I thought I switched my calculator to radians; did 11/60; pressed the arctan button on my calculator (giving me something like 0.18333...). Then, I press the Cosine button to get my answer of 0.983241...) However, the question asks me to find the exact value of cos(arctan11/60), which makes me think it should more be in terms of something like sqrt(2)pi/2 (aka unit circle) format.
For a time, I also considered the answer to be 61/11, but that seems off as well. What is the correct, "exact" answer?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the exact value of cos(arctan11/60)
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Let "t" = arctan(11/60)
Then tan(t) = 11/60
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Since tan(t) = y/x, y = 11 and x = 60
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Then r = sqrt[11^2+60^2] = sqrt(3721) = 61
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Therefore: cos(t) = x/r = 60/61
So cos[arctan(11/60)] = 60/61
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Cheers,
Stan H.
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