Question

Suppose that cot θ = c and 0 < θ < π 2 . what is a formula for cos θ in terms of c?

Answer 1

Answer:

cosθ = c/√1+c²

Step-by-step explanation:

Given cot θ = c and 0 < θ < π/2

In trigonometry identity:

cotθ  = 1/tanθ = c

1/tanθ = c

cross multiply

tanθ  = 1/c

According to SOH, CAH, TOA:

Tanθ = opposite/adjacent = 1/c

cosθ = adjacent/hypotenuse

To get the hypotenuse, we will use the pythagoras theorem:

hyp² = opp²+adj²

hyp² = 1²+c²

hyp = √1+c²

Find cosθ in terms of c

cosθ = c/√1+c²

Hence the formula for cos θ in terms of c is cosθ = c/√1+c²