If sinθ = 1 over 4 and tanθ > 0, what is the value of cosθ?

Solution:

sinθ = 1/4 and tanθ > 0

We can find the adjacent side using the Pythagoras theorem

Hypotenuse² = Adjacent² + Opposite²

Substituting the values

4² = Adjacent² + 1²

Adjacent² = 16 - 1

Adjacent² = 15

Adjacent = √15

Given, tanθ > 0

1/√15 > 0

Both sine and tan are positive.

⇒ θ is the I quadrant. Thus cos is positive.

cosθ = adjacent/hypotenuse

Substitute the values

cosθ = √15/4

Therefore, the value of cosθ is √15/4.

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If sinθ = 1 over 4 and tanθ > 0, what is the value of cosθ?

Summary:

If sinθ = 1 over 4 and tanθ > 0, then the value of cosθ is √15/4.