Question

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

Answer 1

Answer:

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