Question

The terminal side of an angle θ in standard position passes through the point (3, 1). Calculate the exact values of the six trig functions for angle θ.

Answer 1

Answer:

sin α = $\frac{y}{r}$ = $\frac{1}{\sqrt{10} }$

cos α = $\frac{x}{r}$ = $\frac{3}{\sqrt{10} }$

tan α = $\frac{y}{x}$ = $\frac{1}{3}$

cot α = $\frac{x}{y}$ = $\frac{3}{1}$

sec α = $\frac{r}{x}$ = $\frac{\sqrt{10} }{3}$

csc α = $\frac{r}{y}$ = $\frac{\sqrt{10} }{1}$

Step-by-step explanation:

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

r = $\sqrt{x^2+y^2}$

Here it is: $\sqrt{3^2+1^2}$ = $\sqrt{9+1}$ = $\sqrt{10}$

So we have:

x = 3

y = 1

r = $\sqrt{10}$

Now we can calculate all 6 trig, functions:

sin α = $\frac{y}{r}$ = $\frac{1}{\sqrt{10} }$

cos α = $\frac{x}{r}$ = $\frac{3}{\sqrt{10} }$

tan α = $\frac{y}{x}$ = $\frac{1}{3}$

cot α = $\frac{x}{y}$ = $\frac{3}{1}$

sec α = $\frac{r}{x}$ = $\frac{\sqrt{10} }{3}$

csc α = $\frac{r}{y}$ = $\frac{\sqrt{10} }{1}$