Pre Calculus Question

Question

Given 𝑠𝑖𝑛𝜃 = −1 and 𝑐𝑜𝑠𝜃 > 0, find (a) 𝑠𝑖𝑛2𝜃, and (b) 𝑐𝑜𝑠2𝜃

Answer 1

Given sin θ = -1/5 and cos θ > 0, we must have cos θ = √(1 - 1/25) = √24 / 5

a) sin 2θ = 2 sin θ cos θ = 2 * (-1 / 5) * (√24 / 5) = -4 √6 / 25

b) cos 2θ = 1 - 2 (sin θ)² = 23 / 25