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Let's go through each of these exercises one by one:

### 27. \( \sin^{-1}(0.5) \)

- In radians: The inverse sine of \(0.5\) corresponds to an angle of \( \frac{\pi}{6} \).
- In degrees: \( \frac{\pi}{6} \) radians equals **30°**.

### 28. \( \sin^{-1}\left( \frac{-\sqrt{2}}{2} \right) \)

- In radians: \( \sin^{-1}\left( \frac{-\sqrt{2}}{2} \right) \) corresponds to \( -\frac{\pi}{4} \) since \( \sin(-\frac{\pi}{4}) = -\frac{\sqrt{2}}{2} \).
- In degrees: \( -\frac{\pi}{4} \) radians equals **-45°**.

### 29. \( \tan^{-1}(-5) \)

- In radians: The inverse tangent of \( -5 \) doesn't have a simple exact form like the others, so we calculate it numerically: \( \tan^{-1}(-5) \approx -1.3734 \) radians.
- In degrees: \( -1.3734 \) radians equals approximately **-78.69°**.

### 30. \( \cos^{-1}(0.7) \)

- In radians: The inverse cosine of \( 0.7 \) can be computed numerically as \( \cos^{-1}(0.7) \approx 0.7954 \) radians.
- In degrees: \( 0.7954 \) radians equals approximately **45.6°**.

Would you like more details or clarifications on any of these solutions?

Here are 5 related questions for further practice:
1. What is \( \sin^{-1}(-0.5) \) in radians and degrees?
2. Find \( \cos^{-1}(-0.7) \) in both radians and degrees.
3. What is the value of \( \tan^{-1}(1) \) in exact radians?
4. Calculate \( \sin^{-1}\left(\frac{1}{\sqrt{2}}\right) \) and convert to degrees.
5. What is \( \tan^{-1}(5) \) in radians and degrees?

**Tip**: Inverse trigonometric functions are often restricted to specific ranges to give a single, principal value for each input. For example, \( \sin^{-1} \) ranges from \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \).

In Exercises 27–30, give the measure of the angle in radians and degrees. Give exact answers whenever possible.

Learn how to calculate the inverse sine, cosine, and tangent for given values in both radians and degrees. Examples include sin^{-1}(0.5), cos^{-1}(0.7), and tan^{-1}(-5). Suitable for high school trigonometry students.

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