Question

If the sine of an acute angle is 3/5, what is the cosine of that angle?

Answer 1

Answer:

The cosine of the angle is 4/5.

Step-by-step explanation:

An acute angle is between 0º and 90º, in the first quadrant of the trigonometric circle, in which both the sine and the cosine are positive values.

For each angle $\alpha$, we have that:

$\sin^{2}{\alpha} + \cos^{2}{\alpha} = 1$

We have that:

$\sin{\alpha} = \frac{3}{5}$

So

$\sin^{2}{\alpha} + \cos^{2}{\alpha} = 1$

$(\frac{3}{5})^{2} + \cos^{2}{\alpha} = 1$

$\cos^{2}{\alpha} = \frac{16}{25}$

$\cos{\alpha} = \frac{4}{5}$

The cosine of the angle is 4/5.