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

base² = (hypotenuse)² - (perpendicular)² 

base = √(16x² - x²)

base = √(15x²)

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