The straight line y = mx where m > 0 forms an angle of 30^@ with the positive x-axis. What does m equal?

(A) sqrt3

(B) sqrt3/3

(C) 2-sqrt3

(D) None of the above

1 Answer
Apr 5, 2018

Correct answer is sqrt(3)/3.

(C)

Explanation:

By definition, tan(theta)=sin(theta)/cos( theta).
sin(theta) is the y-component in the unit circle and cos(theta) the x component.

Therefore tan(theta) = y/x or the slope of the line.

Since the angle is 30 degrees, tan(30)=m. tan(30°) = 1/sqrt(3).

Rationalize: 1/sqrt(3)*sqrt(3)/sqrt(3) to get sqrt(3)/3.