Question

There is a clown's face on the top of a spinner. The tip of his hat rotates to (−2, 5) during one spin. What is the cosine value of this function?

Answer 1

Remark
The point value is (-2,5) So we know the two sides. We need the hypotenuse. We should notice that the x value is minus (-2) and value is y value is plus (5). That means we are in quad 2. Be careful how you read that. (-2,5) is a point. It is not a tangent.

Step One
Find the hypotenuse.

a = - 2
b = 5
c = ??

c^2 = a^2 + b^2
c^2 = (-2)^2 + 5^2
c^2 = 4 + 25
c^2 = 29 Take the square root of both sides.
sqrt(c^2) = sqrt(29)
c = sqrt(29)

Step Two
Find the Cosine of the angle.
Cosine(theta) = adjacent / hypotenuse
Cosine(theta) = -2 / sqrt(29) <<<<<<< Answer

Again, watch out for what you are given.