Question

For an angle θ with the point (16, −30) on its terminating side, what is the value of cosine?

Answer 1

First, let's locate the point's position in the x-y coordinate. Since x is positive and y is negative, we can place the point in the fourth quadrant. You may check the image so the next steps will be clearer as well.

Seeing that the legs of the right triangle formed are 16 and 30, we can apply the Pythagorean theorem to solve for the triangle's hypotenuse. Hence, we have

hypotenuse = √(16² + 30²) = 34

Recall that the cosine of a triangle's angle is the value of the ratio of the side adjacent to the angle and the triangle's hypotenuse. Or simply, we have


`\cos\theta = (A)/(H)`

`\cos\theta = (-30)/(34)`

`\cos\theta = (-15)/(17)`

Answer: -15/17