If sinθ = 3 over 7 and tanθ < 0, what is the value of cosθ?

Solution:

sinθ = 3/7 and tanθ < 0

So cosθ will be negative

sinθ = 3/7

By squaring on both sides

sin²θ = 9/49

It can be written as

1 - cos²θ = 9/49

cos²θ = 1 - 9/49

By further calculation

cos²θ = 40/49

So we get,

cosθ = ±√40/7

Sin is +ve and tan is negative in the II quadrant. Thus cos is negative in II quadrant.

Therefore, the value of cosθ is -√40/7.

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If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ?

Summary:

If sin θ = 3 over 7 and tan θ < 0, the value of cos θ is -√40/7.