If sinθ = 2 over 7 and tanθ > 0, what is the value of cosθ?

Solution:

Given: sinθ = 2 over 7 and tanθ > 0 hence, cosθ will also be positive.

sinθ = 2/7

By squaring on both sides

sin²θ = 4/49

From the trigonometric identity sin²θ + cos²θ = 1

So we get,

cos²θ = 1 - sin²θ

cos²θ = 1 - 4/49

cos²θ = 45/49

cosθ = √45/7

Therefore, the value of cosθ is √45/7.

If sinθ = 2 over 7 and tanθ > 0, what is the value of cosθ?

Summary:

If sinθ = 2 over 7 and tanθ > 0, then the value of cosθ is √45/7.