Question

fill in each blank so that the resulting statement is true. let θ be any angle in standard position and let p=(x,y) be any point besides the origin on the terminal side of θ. if r = √(x² + y²) is the distance from (0,0) to (x,y), the trigonometric functions of θ are defined as given below. sin θ = cos θ = tan θ = csc θ = sec θ = cot θ =

Explanation:

Step1: Recall sine definition

$\sin\theta=\frac{y}{r}$

Step2: Recall cosine definition

$\cos\theta=\frac{x}{r}$

Step3: Recall tangent definition

$\tan\theta=\frac{y}{x}(x
eq0)$

Step4: Recall cosecant definition

$\csc\theta=\frac{r}{y}(y
eq0)$

Step5: Recall secant definition

$\sec\theta=\frac{r}{x}(x
eq0)$

Step6: Recall cotangent definition

$\cot\theta=\frac{x}{y}(y
eq0)$

Answer:

$\sin\theta=\frac{y}{r}$, $\cos\theta=\frac{x}{r}$, $\tan\theta=\frac{y}{x}(x
eq0)$, $\csc\theta=\frac{r}{y}(y
eq0)$, $\sec\theta=\frac{r}{x}(x
eq0)$, $\cot\theta=\frac{x}{y}(y
eq0)$