Evaluate cscθ if cosθ is....?

Question

Evaluate cscθ if cosθ =1/5, where -π/2 ≤ θ ≤ π/2. Give an exact answer.

Answer 1

In the given range sinθ could be positive or negative and hence cscθ could also be positive or negative. cosθ MUST be positive.

cosθ =1/5

cos²θ = 1/5

sin²θ = 1 - (1/5)² = 24/25

sinθ = ±2√6/5

cscθ = 1/sinθ = ±5/(2√6) = ±5√6/12

Answer 2

hi

  (sinx)^2= 1-(cosx)^2=1-1/25=24/25

  sinx= + - 2(sqr6)/5