Question

If the terminal side of angle 0 in standard position intersects the unit circle at p (3/5,4/5). Find cos0 and sin0

Answer 1

Answer:

$\sin \theta = \frac{4}{5}$, $\cos \theta = \frac{3}{5}$

Step-by-step explanation:

Let be $P(x,y) = \left(\frac{3}{5}, \frac{4}{5} \right)$ the end of the terminal side of angle $\theta$ 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:

$\sin \theta = \frac{y}{\sqrt{x^{2} + y^{2}}}$ (1)

$\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}$ (2)

If we know that $x = \frac{3}{5}$ and $y = \frac{4}{5}$, then the sine and the cosine of the angle are:

$\sin \theta = \frac{\frac{4}{5} }{\sqrt{\left(\frac{3}{5} \right)^{2}+\left(\frac{4}{5} \right)^{2}}}$

$\sin \theta = \frac{4}{5}$

$\cos \theta = \frac{\frac{3}{5} }{\sqrt{\left(\frac{3}{5} \right)^{2}+\left(\frac{4}{5} \right)^{2}}}$

$\cos \theta = \frac{3}{5}$