# 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

Hypotenuse^{2} = Adjacent^{2} + Opposite^{2}

Substituting the values

4^{2} = Adjacent^{2} + 1^{2}

Adjacent^{2} = 16 - 1

Adjacent^{2} = 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.

## 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.

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