Answer
$\cos{\theta} = \dfrac{12}{13}
\\\sin{\theta} = \dfrac{5}{13}$
Work Step by Step
(Assumption: the angle is in standard position)
If the point $(6.36, 2.65)$ is on the terminal side of $\theta$. then $r$ can be solved using the formula:
$r=\sqrt{x^2 + y^2}$
The given point has $x=6.36$ and $y=2.65$. Substitute these values into the formula above to obtain:
$r= \sqrt{6.36^2 + 2.65^2}
\\r = 6.89$
RECALL:
$\sin{\theta} = \dfrac{y}{r}
\\\cos{\theta} = \dfrac{x}{r}$
Use the formulas above and the known values of x, y, and r to obtain:
$\cos{\theta} = \dfrac{6.36}{6.89}=\dfrac{12}{13}
\\\sin{\theta} = \dfrac{2.65}{6.89}=\dfrac{5}{13}$
