Find tan θ if cos θ = one divided by four and sin θ < 0.

Solution:

It is given that

cos θ = one divided by four and sin θ < 0

We can write it as

cos θ = 1/4 and sin θ < 0

θ will be the element of the fourth quadrant i.e 3π / 2 < θ < 2π.

Assume a right angled triangle of base 1 unit and hypotenuse 4 units

As cos θ = Base/ Hypotenuse

cos θ = 1/4

Using the Pythagorean theorem, the perpendicular will be √15 units

tan θ = Perpendicular / Base

tan θ = √15/1 = √15

θ lies in the fourth quadrant so tan θ will be negative.

tan θ = -√15

Therefore, tan θ = -√15.

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Find tan θ if cos θ = one divided by four and sin θ < 0.

Summary:

The value of tan θ if cos θ = one divided by four and sin θ < 0 is -√15.