To find the cosine of an angle θ whose terminating side passes through the point (20, 21), we need to use the definition of cosine in relation to the coordinates of a point in the Cartesian plane.
1. **Understanding the Coordinates:** In this case, the point (20, 21) represents a position on the terminal side of the angle θ in standard position (where the angle is measured from the positive x-axis). The x-coordinate is 20, and the y-coordinate is 21.
2. **Calculating the Radius (r):** The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse. We first need to calculate the radius (r), which is the distance from the origin (0, 0) to the point (20, 21). This can be calculated using the Pythagorean theorem:
r = √(x2 + y2)
r = √(202 + 212)
r = √(400 + 441)
r = √841
r = 29
3. **Calculating Cosine:** Now that we have the radius (hypotenuse of the triangle) as 29, we can find the cosine of the angle θ:
cos(θ) = adjacent/hypotenuse
cos(θ) = x/r
cos(θ) = 20/29
4. **Conclusion:** Therefore, the value of cosine for the angle θ whose terminating side passes through the point (20, 21) is:
cos(θ) = 20/29
This fraction represents the ratio of the x-coordinate to the radius, which is a straightforward way to find the cosine of any angle based on its terminal point.