Question

Determine the slope of a line that makes an angle of 5pi/4 radians with the x-axis.

Answer 1

check the picture.

π radians is the angle 180 degrees, so π/4 radians is 180°/4=45°.

to construct the angle
`5 ( \pi)/(4)` we can proceed as shown in the figure, that is, we open an angle equal to 5 half right angles.

We see that the line making the angle 5pi/4 is the same line making the angle pi/4 radians, that is 45 degrees.

A line making the angle 45 degrees with the x axis, has slope equal to 1.

Remark, we have considered a line passing through the origin, as it represents all other lines making 5pi/4 radians.

Answer: slopi=1