To evaluate a trigonometric ratio for an angle with negative measure using the unit circle, follow these steps:
1. **Understand the Unit Circle**: The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It helps in understanding trigonometric ratios for various angles.
2. **Represent the Negative Angle**: When dealing with a negative angle, think of it as moving clockwise instead of the usual counterclockwise direction. For example, for -45°, visualize moving 45° clockwise from the positive x-axis.
3. **Find the Reference Angle**: The reference angle is the positive acute angle between the terminal side of the angle and the x-axis. For -45°, the reference angle is 45°.
4. **Determine the Trigonometric Ratio**: Look at the corresponding point on the unit circle that aligns with the reference angle (45° in this case). For sin(-45°) or cos(-45°), consider the y-coordinate or x-coordinate of the point, respectively.
5. **Use Symmetry**: Since the unit circle is symmetric, the trigonometric ratios for the negative angle will be the same as the corresponding positive angle but with the signs adjusted accordingly. For sin(-45°), sin(45°) = 1/√2, so sin(-45°) = -1/√2. For cos(-45°), cos(45°) = √2/2, so cos(-45°) = √2/2.
By following these steps and understanding the properties of the unit circle, you can accurately evaluate trigonometric ratios for angles with negative measures.
