Find the reference angle for the given angle.
240°
°

Find the quadrant of the terminal side of the given angle.
Quadrant I
Quadrant II
Quadrant III
Quadrant IV

Find the sine and cosine of the angle. If the angle is not one of the angles on the unit circle, use a calculator and round to three decimal places.
sin(240°)	 =
cos(240°)	 =

Let's solve this step by step:

### 1. **Reference Angle for 240°:**

The reference angle is the smallest angle between the terminal side of the given angle and the x-axis. Since \( 240^\circ \) is in the third quadrant (between \( 180^\circ \) and \( 270^\circ \)), we can find the reference angle by subtracting \( 180^\circ \) from \( 240^\circ \).

\[
\text{Reference angle} = 240^\circ - 180^\circ = 60^\circ
\]

So, the reference angle is **60°**.

### 2. **Quadrant of the Terminal Side:**

The angle \( 240^\circ \) is located in **Quadrant III**, because it's between \( 180^\circ \) and \( 270^\circ \).

### 3. **Sine and Cosine of 240°:**

Since \( 240^\circ \) is in the third quadrant, we know that sine is negative and cosine is negative in this quadrant.

Using the reference angle of \( 60^\circ \), we know:
- \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \)
- \( \cos(60^\circ) = \frac{1}{2} \)

In the third quadrant, sine and cosine both are negative:

\[
\sin(240^\circ) = -\sin(60^\circ) = -\frac{\sqrt{3}}{2} \approx -0.866
\]
\[
\cos(240^\circ) = -\cos(60^\circ) = -\frac{1}{2} = -0.500
\]

Thus:
\[
\sin(240^\circ) \approx -0.866
\]
\[
\cos(240^\circ) = -0.500
\]

### Summary:
- **Reference angle**: 60°
- **Quadrant**: Quadrant III
- **sin(240°)**: -0.866
- **cos(240°)**: -0.500

Would you like further details or clarifications? 

Here are 5 related questions:
1. What is the reference angle for 315°?
2. In which quadrant is the angle 150° located?
3. Find the sine and cosine of 330°.
4. How does the sine and cosine of an angle change in each quadrant?
5. What is the reference angle for an angle of 120°?

**Tip**: Always remember that sine is positive in Quadrants I and II, and cosine is positive in Quadrants I and IV!

Find the reference angle for the given angle 240°. Find the quadrant of the terminal side of the given angle. Find the sine and cosine of the angle. If the angle is not one of the angles on the unit circle, use a calculator and round to three decimal places.

Learn how to find the reference angle, sine, and cosine for 240°. This problem explores key trigonometric concepts such as reference angles, the unit circle, and trigonometric ratios in Quadrant III. Suitable for high school students (Grades 9-12).

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