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How do you evaluate #csc^-1(2)# without a calculator?

Answer 1

James Adkins

30 degree

#csc^-1# (2) = #csc^-1# (csc 30) = 30 degree

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Answer 2

Victoria Adebayo

To evaluate ( \csc^{-1}(2) ) without a calculator, we recall that ( \csc^{-1}(x) ) represents the arc cosecant function, which is the inverse of the cosecant function ( \csc(x) ).

First, we know that ( \csc(x) = \frac{1}{\sin(x)} ). So, if ( \csc^{-1}(2) = \theta ), then ( \sin(\theta) = \frac{1}{2} ).

We can determine where ( \sin(x) = \frac{1}{2} ) by remembering common trigonometric ratios. We know that ( \sin(\frac{\pi}{6}) = \frac{1}{2} ) for ( 0 < x < \pi ).

So, ( \csc^{-1}(2) = \frac{\pi}{6} ).

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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.