Question

The terminal side of θ passes through the point (8,−7).

What is the exact value of cosθ in simplified form?

Answer 1

8√113 / 113

Explanation:

Representing the information on a triangle :

From trigonometry :

Cos θ = Adjacent / hypotenus = AC / AB

AB = hypotenus :

Using Pythagoras :

AB² = AC² + BC²

AB² = 8² + (-7)²

AB² = 64 + 49

AB = √113

Cos θ = AC / AB = 8 / √113

RATIONALIZE :

8/√113 * √113/√113 = 8√113 / 113