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How do you find the exact values of COS(-337.5) using the half angle formula?

Answer 1

Find cos (-337.5)
Answer: #+- sqrt(2 + sqrt2)/2#

Call cos (-337.5) = cos t --> cos (2t) = cos (675) Apply the trig identity: cos 2t = 2cos^2 t - 1 On the trig unit circle, #cos (2t) = cos (675) = cos (-45 + 2(360)) = cos 45 = sqrt2/2#

Therefor, #sqrt2/2 = 2cos^2 t - 1# --> #cos^2t = (2 + sqrt2)/4#->

#cos t = cos (-337.5) = +- sqrt(2 + sqrt2)/2#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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