techdeckdude1237 techdeckdude1237

22-12-2020
Mathematics

contestada

Given sinθ = 2/5 and cosθ < 0:
1. Find cscθ
2. Find cotθ

Respuesta :

LammettHash LammettHash

22-12-2020

Recall that

sin²(θ) + cos²(θ) = 1

for all θ, and given that cos(θ) < 0, we find that

cos(θ) = -√(1 - sin²(θ)) = -√(1 - (2/5)²) = -√(21)/5

Now,

csc(θ) = 1/sin(θ) = 1/(2/5) = 5/2

and

cot(θ) = cos(θ)/sin(θ) = (-√(21)/5)/(2/5) = -√(21)/2

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