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!