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

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

## Answer: The value of cos θ calculated is 0.9682

Go through the steps to understand better.

**Explanation:**

Given, tan θ > 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 sine, so we need to calculate the value of cos in the 1^{st} quadrant itself.

sin θ = 1/4 = perpendicular / hypotenuse

On multiplying x on both numerator and denominator, 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 = sqrt (16x^{2} - x^{2})

base = sqrt (15x^{2})

base = sqrt(15) × x

cos θ = base / hypotenuse

cos θ = (sqrt(15) × x) / 4x

cos θ = 0.9682

cosine of this angle comes out to be 0.9682