Question

find all angles θ between 0° and 180° satisfying the given equation. round your answer to one decimal place. (enter your answers as a comma - separated list.) sin(θ) = 2/7

Explanation:

Step1: Use inverse - sine function

$\theta=\sin^{-1}(\frac{2}{7})$

Step2: Calculate the principal value

$\theta_1=\sin^{-1}(\frac{2}{7})\approx16.6^{\circ}$

Step3: Find the second - angle in the range $[0^{\circ},180^{\circ}]$

Since $\sin\theta=\sin(180^{\circ}-\theta)$, the second angle $\theta_2 = 180^{\circ}-\sin^{-1}(\frac{2}{7})\approx180 - 16.6=163.4^{\circ}$

Answer:

$16.6^{\circ},163.4^{\circ}$