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How do you find the exact value of #cos(arccos(0.25))#?

Answer 1

Elijah Alexander

#0.25#

#Cos(arccos(0.25))#

#:.=Cos(75.52248781^@) or 75^2 31'20.9''#

#:.=0.25#

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Answer 2

Caroline Adams

To find the exact value of ( \cos(\arccos(0.25)) ), you can use the fact that ( \arccos(\cos(x)) = x ) for ( 0 \leq x \leq \pi ). So, ( \arccos(0.25) ) is the angle whose cosine is ( 0.25 ). Using this, you can find the angle, then evaluate the cosine of that angle. ( \arccos(0.25) ) is approximately ( 1.3181 ) radians or ( 75.5225^\circ ). So, ( \cos(\arccos(0.25)) = \cos(1.3181) ) or ( \cos(75.5225^\circ) ). Since ( \cos(75.5225^\circ) ) is a special angle, it equals ( \frac{\sqrt{6} - \sqrt{2}}{4} ) or approximately ( 0.9063 ).

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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.