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 [tex]\alpha[/tex], we have that:
[tex]\sin^{2}{\alpha} + \cos^{2}{\alpha} = 1[/tex]
We have that:
[tex]\sin{\alpha} = \frac{3}{5}[/tex]
So
[tex]\sin^{2}{\alpha} + \cos^{2}{\alpha} = 1[/tex]
[tex](\frac{3}{5})^{2} + \cos^{2}{\alpha} = 1[/tex]
[tex]\cos^{2}{\alpha} = \frac{16}{25}[/tex]
[tex]\cos{\alpha} = \frac{4}{5}[/tex]
The cosine of the angle is 4/5.
