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svp [43]
2 years ago
14

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

Mathematics
1 answer:
Tems11 [23]2 years ago
5 0

Recall that

sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1

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

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

Now,

csc(<em>θ</em>) = 1/sin(<em>θ</em>) = 1/(2/5) = 5/2

and

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

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