If secant theta is equal to negative square root of 34, over 3 and sine theta is greater than zero, then find the exact value of cosecant theta.

Answer 1

cosθ = 1/secθ = 1/(-√34/3) = -3/√34

Then, sinθ > 0, so sinθ = √(1 - ( -3/√34)²) = √(1 - 9/34) = √(25/34) = 5/√34, so

cscθ = 1/sinθ = 1/(5/√34) = √34/5