Angle θ is an acute angle of a right triangle. Determine the value of cot θ given the value of sin θ below. what is sin θ 15/17?

Answer 1

To determine the value of cot θ, we need to find the cosine of θ. We can use the Pythagorean identity to find the cosine:

cos²θ = 1 - sin²θ

Since sinθ = 15/17, we can substitute this value in:

cos²θ = 1 - (15/17)²
cos²θ = 1 - 225/289
cos²θ = 289/289 - 225/289
cos²θ = 64/289

Taking the square root of both sides, we get:

cosθ = ±8/17

Since θ is an acute angle, cosine is positive, so:

cosθ = 8/17

Finally, we can find the cotangent:

cotθ = cosθ / sinθ
cotθ = (8/17) / (15/17)
cotθ = 8/15

Therefore, cotθ = 8/15.