Question

30.) use your calculator to evaluate the following to the nearest tenth.
a.) $\sin^{-1}(\frac{2}{7}) =$____ b.) $\cos^{-1}(-\frac{2}{3}) =$__ c.) $\tan^{-1}(5) =$__ d.) $\sin^{-1}(5) =$____

Explanation:

Step1: Evaluate \( \sin^{-1}(\frac{2}{7}) \)

Using a calculator in degree mode (assuming standard unless specified otherwise), \( \sin^{-1}(\frac{2}{7})\approx16.6^{\circ} \)

Step2: Evaluate \( \cos^{-1}(-\frac{2}{3}) \)

Using a calculator in degree mode, \( \cos^{-1}(-\frac{2}{3})\approx131.8^{\circ} \)

Step3: Evaluate \( \tan^{-1}(5) \)

Using a calculator in degree mode, \( \tan^{-1}(5)\approx78.7^{\circ} \)

Step4: Evaluate \( \sin^{-1}(5) \)

Since the domain of \( y = \sin^{-1}(x)\) is \(x\in[- 1,1]\), and \(5
otin[-1,1]\), \( \sin^{-1}(5)\) is undefined.

Answer:

a. \(16.6^{\circ}\)
b. \(131.8^{\circ}\)
c. \(78.7^{\circ}\)
d. Undefined