Question

Solve sin(x) = 0.23 on 0 ≤ x < 2T.There are two solutions, A and B, with A

Answer 1

Given -

sin(x) = 0.23 on 0 ≤ x < 2π

To Find -

Two solutions, A and B =?

Step-by-Step Explanation -

$0.23\text{ = }\frac{23}{100}$

So, the two solutions will be -

$\begin{gathered} \sin^{-1}(\frac{23}{100})\text{ and }\pi\text{ - }\sin^{-1}(\frac{23}{100}) \\ \\ So,\text{ }\sin^{-1}(\frac{23}{100})\text{ = 0.232} \\ \\ Also,\text{ }\pi\text{ - }\sin^{-1}(\frac{23}{100})\text{ = 3.141 - 0.232 = 2.909} \end{gathered}$

Now, Since A < B

So,

A = 0.232

B = 2.909

Final Answer -

A = 0.232

B = 2.909