To evaluate cosine values for different angles, follow these steps:
Convert the angle to radians if necessary. Many calculators and math functions use radians by default, so it's essential to be comfortable working with radians.
Use the unit circle to determine the cosine value. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) on the coordinate plane. Each point (x, y) on the unit circle corresponds to an angle. The x-coordinate of the point gives the cosine value for that angle.
For common angles (0°, 90°, 180°, etc.), memorize their cosine values. For other angles, use trigonometric functions or tables to find the cosine value.
Here are a few examples:
To evaluate cos(30°), convert it to radians: 30° = π/6 radians. On the unit circle, the point corresponding to this angle is (√3/2, 1/2), so cos(30°) = √3/2.
For cos(π/3), the angle in radians is already given. On the unit circle, the point corresponding to this angle is (1/2, √3/2), so cos(π/3) = 1/2.
Remember to practice evaluating cosine for different angles to reinforce your understanding and gain fluency in working with trigonometric functions!