Question

if the angle θ is in standard position and p(x, y) is a point on the terminal side of θ, and r is the distance from the origin to p, then sin(θ) = cos(θ) = tan(θ) = resources read it submit answer 42. -/0.35 points 0/5 submissions used details my notes ask your teacher

Explanation:

Step1: Recall trigonometric - ratio definitions

By the right - triangle definition of trigonometric functions in a coordinate system, where $r=\sqrt{x^{2}+y^{2}}$.

Step2: Find $\sin(\theta)$

$\sin(\theta)=\frac{y}{r}$ (opposite over hypotenuse in right - triangle formed with the x - axis).

Step3: Find $\cos(\theta)$

$\cos(\theta)=\frac{x}{r}$ (adjacent over hypotenuse in right - triangle formed with the x - axis).

Step4: Find $\tan(\theta)$

$\tan(\theta)=\frac{y}{x}$ ($x
eq0$), as $\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}=\frac{\frac{y}{r}}{\frac{x}{r}}=\frac{y}{x}$.

Answer:

$\sin(\theta)=\frac{y}{r}$, $\cos(\theta)=\frac{x}{r}$, $\tan(\theta)=\frac{y}{x}$