Cos(theta)=1/4, theta is in quadrant 4. Find tan(theta-π/4)

Question

Gave cos, and quadrant, asking to find tangent

algebra 2 class

Answer 1

I do not usually answer questions already answered by other tutors. In this case I was working on this problem before I knew Mark had answered it.

However, the question asks for tan[θ-(π/4)], not for the tan θ.

Probably the easiest way to the tan of the difference is to use the difference formula:

tan(a-b) = (tan a - tan b)/(1+tan a tan b)

In this case this become [-sqrt(15)-1][1- sqrt(15)] = 1.69614.

Answer 2

Draw and label a diagram!√

cos θ = 0.25 in Q IV

sin θ = -√15 / 4

tan θ = ?