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What is the domain and range of #cos^-1 [sqrt(1/4 - x^2)]?#?

Answer 1

Dylan Arnold

Domain: #-1/2 <= x <= 1/2# Range: #pi/3 <= y <= pi/2#

Find the domain,

#1/4 - x^2 >= 0#

#x^2 <= 1/4#

#-1/2 <= x <= 1/2#

This makes the argument of the inverse cosine function vary from

#cos^-1(0) to cos^-1(1/2)#

#pi/2 to pi/3#

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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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