The angle θ=π3 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.

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

Part a

theta = pi/3

sin(pi/3) = sqrt(3)/2

cos(pi/3) = 1/3

tan(angle) = opposite/adjacent = rise/run = slope

tan(pi/3) = sin(pi/3)/cos(pi/3) = (sqrt(3)/2)/(1/2) = sqrt(3)

This is also the slope the line y = kx because it is in the form y = mx+b with m = sqrt(3) and b = 0.

Part b

Pick any value you want for x, and plug it in to find the paired value of y

if x = 0, then y = 0 because

y = sqrt(3)*x = sqrt(3)*0 = 0

If x = 1, then y = sqrt(3), since,

y = sqrt(3)*x = sqrt(3)*1 = sqrt(3)

If x = sqrt(3), then,

y = sqrt(3)*x = sqrt(3)*sqrt(3) = sqrt(3*3) = sqrt(9) = 3

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}