Question

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

Answer 1

Answer:

0.97

Step-by-step explanation:

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

$tan(x)=\frac{sin(x)}{cos(x)} =\frac{1}{4} \\\frac{1}{4}cos(x)=sin(x)$

Applying the following property:

$sin^2(x) +cos^2(x) = 1\\(\frac{1}{4}cos(x))^2 +cos^2(x) = 1\\\\\frac{17}{16}cos^2(x) = 1 \\cos(x)=0.97$

The cosine of that angle is 0.97.