If sinθ = 11 /61, find the values of cosθ using trigonometric identity

We can use the Pythagorean identity to solve for cosθ:

sin^2θ + cos^2θ = 1

Plugging in sinθ = 11/61, we get:

(11/61)^2 + cos^2θ = 1

Simplifying and solving for cosθ, we get:

cosθ = ±sqrt(1 – (11/61)^2)

cosθ = ±(60/61)

Since we are given that θ is in the first quadrant (sinθ is positive), we can take the positive value:

cosθ = 60/61

Therefore, the value of cosθ is 60/61.