Question

The angle θ=π/6 is in standard position and has a terminal side that coincides with the graph of a proportional relationship represented by y=kx.
a. Find the constant of proportionality, k.

k= ?

Question 2
b. Write an ordered pair that lies on the graph of y=kx.

(3√ 3, ? )

Answer 1

Answer:

a) $k \approx \frac{\sqrt{3}}{3}$, b) $\left(\frac{\sqrt{3}}{3}, \frac{1}{3} \right)$

Step-by-step explanation:

a) The constant of proportionality is:

$k = \frac{y}{x}$

$k = \tan \theta$

$k = \tan \frac{\pi}{6}$

$k \approx \frac{\sqrt{3}}{3}$

b) The ordered pair is:

$\left(\frac{\sqrt{3}}{3},\frac{\sqrt{3}}{3}\cdot \frac{\sqrt{3}}{3} \right)$

$\left(\frac{\sqrt{3}}{3}, \frac{1}{3} \right)$