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Let's go through the questions step by step:

### Part (a)
We need to **find an angle coterminal** to \( -\frac{3\pi}{4} \) that lies between \( 0 \) and \( 2\pi \).

Coterminal angles are found by adding or subtracting multiples of \( 2\pi \). To find a positive angle, we can add \( 2\pi \) to \( -\frac{3\pi}{4} \):

\[
-\frac{3\pi}{4} + 2\pi = -\frac{3\pi}{4} + \frac{8\pi}{4} = \frac{5\pi}{4}
\]

Thus, the coterminal angle is \( \frac{5\pi}{4} \), which is between 0 and \( 2\pi \).

### Part (b)
We need to find four positive angles in different quadrants that have the same reference angle as \( -\frac{3\pi}{4} \) and determine whether the cosine or sine is the same.

The reference angle of \( -\frac{3\pi}{4} \) is \( \frac{\pi}{4} \), since it’s the angle from the x-axis to the terminal side, ignoring the direction.

Let's now find the angles in different quadrants:

#### Quadrant I (QI):
In QI, the reference angle is the same as the actual angle.
\[
\text{Angle in QI: } \frac{\pi}{4}
\]
In this quadrant, cosine is positive, so:
\[
\text{Same cosine as } \cos\left(-\frac{3\pi}{4}\right)? \text{No}
\]

#### Quadrant II (QII):
In QII, the angle with the same reference angle is:
\[
\text{Angle in QII: } \pi - \frac{\pi}{4} = \frac{3\pi}{4}
\]
In this quadrant, cosine is negative, so:
\[
\text{Same cosine as } \cos\left(-\frac{3\pi}{4}\right)? \text{Yes}
\]

#### Quadrant III (QIII):
In QIII, the angle is:
\[
\text{Angle in QIII: } \pi + \frac{\pi}{4} = \frac{5\pi}{4}
\]
In this quadrant, sine is negative, so:
\[
\text{Same sine as } \sin\left(-\frac{3\pi}{4}\right)? \text{Yes}
\]

#### Quadrant IV (QIV):
In QIV, the angle is:
\[
\text{Angle in QIV: } 2\pi - \frac{\pi}{4} = \frac{7\pi}{4}
\]
In this quadrant, sine is negative, so:
\[
\text{Same sine as } \sin\left(-\frac{3\pi}{4}\right)? \text{No}
\]

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

### Related Questions:
1. How do you find the reference angle for a given angle?
2. What is the difference between reference angles and coterminal angles?
3. Why is cosine positive in Quadrant I but negative in Quadrant II?
4. How does the unit circle help in determining the signs of trigonometric functions in different quadrants?
5. Can an angle have more than one coterminal angle?

### Tip:
Remember that coterminal angles can be found by adding or subtracting multiples of \( 2\pi \), and reference angles are always positive, measured from the x-axis.

Find each of the following: (a) Find an angle coterminal to -3π/4 that lies between 0 and 2π. (b) Find four positive angles in different quadrants, with the same reference angle as -3π/4, and determine whether they have the same cosine or sine.

Learn how to find the coterminal angle to -3π/4 that lies between 0 and 2π. Additionally, explore how to determine four angles in different quadrants with the same reference angle as -3π/4, identifying whether they have the same cosine or sine. This problem covers key trigonometry concepts and quadrant properties.

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