https://file.aiquickdraw.com/mathbot/file/1726879606547t94iqv4x.jpg

Let's solve both parts of the problem shown in the image:

### (a) Find an angle between \(0^\circ\) and \(360^\circ\) that is coterminal with \(1170^\circ\):

To find a coterminal angle between \(0^\circ\) and \(360^\circ\), we need to subtract multiples of \(360^\circ\) from \(1170^\circ\) until the result is between \(0^\circ\) and \(360^\circ\).

\[
1170^\circ \mod 360^\circ = 1170^\circ - (360^\circ \times 3) = 1170^\circ - 1080^\circ = 90^\circ
\]

So, the coterminal angle between \(0^\circ\) and \(360^\circ\) that is coterminal with \(1170^\circ\) is \(90^\circ\).

### (b) Find an angle between \(0\) and \(2\pi\) that is coterminal with \(-5\pi\):

Here, the goal is to find an angle coterminal with \(-5\pi\) between \(0\) and \(2\pi\). Since \(2\pi\) is the full circle, we can add \(2\pi\) repeatedly to bring the angle into the required range:

\[
-5\pi + (2\pi \times 3) = -5\pi + 6\pi = \pi
\]

Thus, the coterminal angle between \(0\) and \(2\pi\) is \(\pi\).

### Summary:
- (a) The coterminal angle with \(1170^\circ\) between \(0^\circ\) and \(360^\circ\) is \(90^\circ\).
- (b) The coterminal angle with \(-5\pi\) between \(0\) and \(2\pi\) is \(\pi\).

Would you like further details or explanations?

Here are 5 related questions:
1. What are coterminal angles?
2. How do you find coterminal angles in radians?
3. Can angles greater than \(360^\circ\) or \(2\pi\) still be used in trigonometric functions?
4. How does the unit circle help in understanding coterminal angles?
5. What is the difference between positive and negative angles when finding coterminal angles?

**Tip:** Always remember that to find coterminal angles, adding or subtracting multiples of \(360^\circ\) (or \(2\pi\)) is the key step!

Find an angle between 0° and 360° that is coterminal with 1170°. Find an angle between 0 and 2π that is coterminal with −5π.

Learn how to find coterminal angles for 1170° in degrees and −5π in radians. This problem covers key trigonometric concepts and formulas, suitable for students in Grades 10-12.

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