# If sin θ = 1 over 4 and tan θ > 0, what is the value of cos θ?

We can make use of the trigonometric ratios to calculate different angle values easily.

## Answer: If sin θ = 1 over 4 and tan θ > 0, the value of cos θ is 0.9682

Go through the steps to understand better.

**Explanation:**

Given, tan θ > 0 and sin θ = 1/4 > 0

Since tangent is positive in the first and the third quadrant, and sine is positive in the first and second quadrant.

Thus, 1^{st} quadrant is common in both tan and sin, so we need to calculate the value of cos in the 1^{st} quadrant itself.

sin θ = 1/4 = perpendicular / hypotenuse

On multiplying x with both numerator and denominator of 1/4, we get

sin θ = x/4x = perpendicular / hypotenuse

Thus, perpendicular = x, hypotenuse = 4x

Applying the Pythagoras theorem, we get

base^{2} = (hypotenuse)^{2 }- (perpendicular)^{2 }

base = √(16x^{2} - x^{2})

base = √(15x^{2})

base = x√(15)

cos θ = base / hypotenuse

cos θ = (x√15) / 4x

cos θ = 0.9682

cosine of this angle comes out to be 0.9682

### Thus, the value of cos θ calculated is 0.9682

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