SOLUTION: The line y = x/2 makes an angle w with the positive x-axis. The line y = mx makes an angle 2w with the positive x-axos. Compute m. Should be solved without the use of a calculator.

Algebra ->  Trigonometry-basics -> SOLUTION: The line y = x/2 makes an angle w with the positive x-axis. The line y = mx makes an angle 2w with the positive x-axos. Compute m. Should be solved without the use of a calculator.      Log On


   

Question 1177383: The line y = x/2 makes an angle w with the positive x-axis. The line y = mx makes an angle 2w with the positive x-axos. Compute m. Should be solved without the use of a calculator.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The line y+=+x%2F2+ has the slope of 1%2F2 or 0.5.

Hence, the angle w is such that tan%28w%29+=+0.5, i.e. w+=+tan%5E-1%280.5%29.
most important in solving this problem is the fact that the slope is the tangent of the angle
m=tan%282w%29
Then
tan%282w%29+=+%282%2Atan%28w%29%29%2F%281-tan%5E2%28w%29%29
tan%282w%29=+%282%2A0.5%29%2F%281-0.5%5E2%29
tan%282w%29+=+1%2F%281-1%2F4%29+
tan%282w%29+=+1%2F%28%283%2F4%29%29+
tan%282w%29=+4%2F3

Thus m++=+4%2F3.