To find the sine and cosine of $225^\circ$:

Step 1: Determine the quadrant of the angle

• The angle $225^\circ$ lies in the third quadrant because it is between $180^\circ$ and $270^\circ$.

Step 2: Reference angle

• The reference angle is $225^\circ - 180^\circ = 45^\circ$.
• In the third quadrant, sine and cosine are both negative.

Step 3: Evaluate the sine and cosine

• $\sin(45^\circ) = \frac{\sqrt{2}}{2}$, but since it's in the third quadrant, $\sin(225^\circ) = -\frac{\sqrt{2}}{2} \approx -0.707$.
• $\cos(45^\circ) = \frac{\sqrt{2}}{2}$, but since it's in the third quadrant, $\cos(225^\circ) = -\frac{\sqrt{2}}{2} \approx -0.707$.

Final answers:

• $\sin(225^\circ) = -0.707$
• $\cos(225^\circ) = -0.707$

Do you want more details or have any questions?

Here are 5 related questions:

1. What are the sine and cosine of $315^\circ$?
2. How do you find the tangent of an angle using sine and cosine?
3. What are the exact values of sine and cosine for angles in the unit circle?
4. How do you convert an angle from degrees to radians?
5. Why are sine and cosine negative in certain quadrants?

Tip: Always remember that sine and cosine are based on the x- and y-coordinates of points on the unit circle. This helps with understanding their signs in different quadrants!