To find the value of \(\theta\) such that \(\sin \theta = -0.3\), we need to solve for \(\theta\).

1. The sine function is periodic, so there can be multiple solutions for \(\theta\). We'll first find the principal solution using the inverse sine function:

\[
\theta = \sin^{-1}(-0.3)
\]

2. Using a calculator to find the inverse sine:

\[
\theta = \sin^{-1}(-0.3) \approx -0.3047 \text{ radians}
\]

This is the principal solution in radians. However, since sine is negative in the third and fourth quadrants, we need to consider the periodicity of sine:

- The general solutions in radians are:
\[
\theta = -0.3047 + 2n\pi \quad \text{or} \quad \theta = \pi + 0.3047 + 2n\pi
\]
where \(n\) is any integer, accounting for the periodic nature of the sine function.

3. If you prefer the solution in degrees, you can convert from radians:

\[
\theta \approx -0.3047 \times \frac{180}{\pi} \approx -17.47^\circ
\]

The general solutions in degrees are:
\[
\theta = -17.47^\circ + 360^\circ n \quad \text{or} \quad \theta = 180^\circ + 17.47^\circ + 360^\circ n
\]

Would you like further details or have any specific questions?

Here are 5 related questions you might consider:
1. What are the solutions for other trigonometric functions, like \(\cos \theta = -0.3\)?
2. How can we find \(\theta\) when \(\sin \theta = 0.3\) instead of \(-0.3\)?
3. How do we handle solving trigonometric equations over specific intervals?
4. How does the periodicity of sine and cosine functions affect their solutions?
5. How do you convert between radians and degrees?

**Tip:** When solving trigonometric equations, always consider the periodic nature of the functions to find all possible solutions.

Find the solutions for sin θ = −0.3 by using the inverse sine function. Learn how to calculate the principal and general solutions, along with the conversion between radians and degrees. This problem covers key trigonometric concepts suitable for students in Grades 10-12.

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