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.
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, 1st quadrant is common in both tan and sin, so we need to calculate the value of cos in the 1st quadrant itself.
sin θ = 1/4 = perpendicular / hypotenuse
sin θ = x/4x = perpendicular / hypotenuse
Thus, perpendicular = x, hypotenuse = 4x
Applying the Pythagoras theorem, we get
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