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:

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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