Question

use a calculator to find the values of the inverse trigonometric functions. round to the nearest degree.
\\( \sin ^ { - 1 } \left( \frac { 2 } { 3 } \
ight) = \square ^ { \circ } \\)
\\( \tan ^ { - 1 } ( 4 ) = \square ^ { \circ } \\)
\\( \cos ^ { - 1 } ( 0.1 ) = \square ^ { \circ } \\)

Explanation:

Step1: Calculate $\sin^{-1}(\frac{2}{3})$

Using a calculator, $\sin^{-1}(\frac{2}{3})\approx42^{\circ}$ (since $\sin(42^{\circ})\approx0.6691\approx\frac{2}{3}$)

Step2: Calculate $\tan^{-1}(4)$

Using a calculator, $\tan^{-1}(4)\approx76^{\circ}$ (since $\tan(76^{\circ})\approx4.0108\approx4$)

Step3: Calculate $\cos^{-1}(0.1)$

Using a calculator, $\cos^{-1}(0.1)\approx84^{\circ}$ (since $\cos(84^{\circ})\approx0.1045\approx0.1$)

Answer:

$\sin^{-1}(\frac{2}{3}) = 42^{\circ}$
$\tan^{-1}(4)=76^{\circ}$
$\cos^{-1}(0.1)=84^{\circ}$