Question

If csc(θ)= 17/15, then what is cos(θ)?
a. 8/15
b. 15/17
c. 8/17
d. 17/8

Answer 1

To find cos(θ) when given csc(θ), we can use the identity cos²(θ) + sin²(θ) = 1. By substituting the value of csc(θ) into the identity, we can find cos(θ) = 8/17.

Step-by-step explanation:

To find cos(θ), we can use the identity: cos²(θ) + sin²(θ) = 1. Given that csc(θ) = 17/15, we can find sin(θ) by taking the reciprocal of csc(θ). So, sin(θ) = 15/17. Using this value, we can substitute it into the identity to find cos(θ):

cos²(θ) + (15/17)² = 1

cos²(θ) + 225/289 = 1

cos²(θ) = 1 - 225/289

cos²(θ) = 64/289

cos(θ) = ±√(64/289)

Since cos(θ) is positive (since csc(θ) is positive), we can conclude that cos(θ) = √(64/289) = 8/17