Final answer:
Cosine of an angle θ is evaluated using the ratio of the x-coordinate to the hypotenuse of the right triangle formed with the point on the terminal side. For the point (-5,6), the hypotenuse is √61, so cos(θ) is -5/√61.
Step-by-step explanation:
To evaluate the cosine of an angle θ given a point on its terminal side, you can use the definition of cosine in a right-angled triangle or in the unit circle concept of trigonometry. Given the point (-5,6), we can determine the cosine by finding the ratio of the x-coordinate (representing the adjacent side in a right-angled triangle) to the hypotenuse (an imaginary line from the origin to the point).
In this case, to find the hypotenuse, we use the Pythagorean theorem:
hypotenuse = √((-5)2 + 62) = √(25 + 36) = √61
Then, cos(θ) = x-coordinate/hypotenuse = -5/√61. To get the decimal value, you would calculate this expression with a calculator.