Question

If the tangent of an acute angle is 1/4, what is the cosine of that angle?

Answer 1

0.97

Explanation:

It is known that the tangent of an angle is given by the quotient between its sine and its cosine.

`tan(x)=(sin(x))/(cos(x)) =(1)/(4) \\(1)/(4)cos(x)=sin(x)\\`

Applying the following property:

`sin^2(x) +cos^2(x) = 1\\((1)/(4)cos(x))^2 +cos^2(x) = 1\\\\(17)/(16)cos^2(x) = 1 \\cos(x)=0.97`

The cosine of that angle is 0.97.