Question

use the aleks calculator to evaluate each expression. give your answers in radians. round them to the nearest hundredth. if applicable, click on \undefined.\ \\( cos^{-1}(-1.08) = square \\) \\( sin^{-1}(0.78) = square \\) \\( \tan^{-1}(-0.27) = square \\)

Explanation:

Step1: Evaluate $\cos^{-1}(-1.08)$

The domain of the inverse cosine function $\cos^{-1}(x)$ is $[-1, 1]$. Since $-1.08$ is not in this interval, $\cos^{-1}(-1.08)$ is undefined.

Step2: Evaluate $\sin^{-1}(0.78)$

Using a calculator (in radian mode), we find $\sin^{-1}(0.78)\approx0.89$ (rounded to the nearest hundredth).

Step3: Evaluate $\tan^{-1}(-0.27)$

Using a calculator (in radian mode), we know that $\tan^{-1}(-x)=-\tan^{-1}(x)$. So $\tan^{-1}(-0.27)=-\tan^{-1}(0.27)\approx - 0.26$ (rounded to the nearest hundredth).

Answer:

$\cos^{-1}(-1.08)=\text{Undefined}$; $\sin^{-1}(0.78)\approx\boldsymbol{0.89}$; $\tan^{-1}(-0.27)\approx\boldsymbol{-0.26}$