What is the exact value of the expression $sin^(-1) (sin^(-1)(-pi/3))$ ?

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Answer 1 · 2018-03-14T20:45:46

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For our situation of $sin^-1(sin^-1(-pi/3))$ , we are asking ourselves: $"In our unit circle definition, what angle gives us the hight of"$ $-pi/3?$

Just note here that $-pi/3~~-1.0471975511965976$

The maximum height a point on the unit circle can maintain is $1$ . (Similarly, the minimum is $-1$ ).

No angle value can give you a value less than $-1$ .

Therefore, no angle satisfies our requirement.

What is the exact value of the expression sin^(-1) (sin^(-1)(-pi/3))sin^(-1) (sin^(-1)(-pi/3)) ?