If tan theta equals - 5/2 and theta is a quadrant II angle, what is cos theta?

cos θ = - 2/√29

Step-by-step 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