Question 5.5.7: Evaluating the inverse functions with a calculator Find the ...

Precalculus Functions and Graphs

Evaluating the inverse functions with a calculator

Find the approximate value of each expression rounded to four decimal places.

.a. $\sin ^{-1}(0.88)$ b. arccot(2.4) c. $\csc ^{-1}(4)$ d. $\cot ^{-1}(0)$

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a. Use the inverse sine function in radian mode to get $\sin ^{-1}(0.88) \approx 1.0759$

b. Use the identity $\cot ^{-1}(x)=\tan ^{-1}(1 / x)$ because 2.4 > 0:

\operatorname{arccot}(2.4)=\tan ^{-1}\left(\frac{1}{2.4}\right) \approx 0.3948

c. $\csc ^{-1}(4)=\sin ^{-1}(0.25) \approx 0.2527$

d. The value of $\cot ^{-1}(0)$ cannot be found on a calculator. But we know that $\cot(π/2) = 0$ and π/2 is in the range (0, π) for $\cot ^{-1}$ , so we have $\cot ^{-1}(0)=\pi / 2$ .

The expressions in parts (a), (b), and (c) are shown on a graphing calculator in Fig. 5.79.

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