Question

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

Answer 1

For this case we have the following equation:
 cot θ = c
 Rewriting we have:
 cosine (θ) / sine (θ) = c
 From here, we must clear the value of the sinus (θ).
 We have then:
 sine (θ) = (1 / c) * cosine (θ)
 Answer:
 a formula for sin θ in terms of c is:
 sine (θ) = (1 / c) * cosine (θ)

Answer 2

Answer:

Sinθ = 1/√c²+1 in terms of c

Step-by-step explanation:

Given cotθ = c and 0 < θ < 2π

Cot θ = 1/tanθ = c

tanθ = 1/c

From SOH, CAH, TOA

tanθ = opposite/adjacent = 1/c

This shows that opposite = 1

adjacent = c

Sinθ = opposite/hypothenuse

Before we can get sinθ, we need the hypotenuse side. Using Pythagoras theorem to get the hypotenuse. According to the theorem, adj²+opp² = hyp²

hyp² = c²+1²

hyp² = c²+1

hyp = √c²+1

Sinθ = 1/√c²+1 in terms of c