Answer:
cos θ = -2/√29
Explanation:
tan θ = -5/2, π/2 < θ < π
One method is to draw a triangle with the hypotenuse in quadrant II. The height of the triangle is 5, and the base is -2. The hypotenuse can be found using Pythagorean theorem:
c² = a² + b²
c² = (-2)² + (5)²
c = √29
Therefore, cos θ = -2/√29.
Another method is to use one of the Pythagorean identities.
tan²θ + 1 = sec²θ
(-5/2)² + 1 = sec²θ
25/4 + 1 = sec²θ
29/4 = sec²θ
cos²θ = 4/29
cos θ = -2/√29