Answer:
[tex]\sin \theta = \frac{4}{5}[/tex], [tex]\cos \theta = \frac{3}{5}[/tex]
Step-by-step explanation:
Let be [tex]P(x,y) = \left(\frac{3}{5}, \frac{4}{5} \right)[/tex] the end of the terminal side of angle [tex]\theta[/tex] in standard position, that is, an angle measured with respect to +x semiaxis. By Trigonometry, we know that the sine and the cosine of the angle are, respectively:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2} + y^{2}}}[/tex] (1)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
If we know that [tex]x = \frac{3}{5}[/tex] and [tex]y = \frac{4}{5}[/tex], then the sine and the cosine of the angle are:
[tex]\sin \theta = \frac{\frac{4}{5} }{\sqrt{\left(\frac{3}{5} \right)^{2}+\left(\frac{4}{5} \right)^{2}}}[/tex]
[tex]\sin \theta = \frac{4}{5}[/tex]
[tex]\cos \theta = \frac{\frac{3}{5} }{\sqrt{\left(\frac{3}{5} \right)^{2}+\left(\frac{4}{5} \right)^{2}}}[/tex]
[tex]\cos \theta = \frac{3}{5}[/tex]
