Question

Find the slope of the line passing through the origin at an angle 5π/8. What angle is this in degrees?

Do I just literally type `tan(5\pi )/(8)` into my calculator and get the answer as 0.034 degrees?

Answer 1

See below.

Explanation:

The slope of a line is given as a tangent ratio. In this case you have the angle, so the slope would be given as `tan((5pi)/8)`.

The angle the line makes with the horizontal is given in radians here:

`(5pi)/8`

If you want this in degrees you can use:

`180^@=picolor(white)(8) "radians"`

`1color(white)(88) "radian" = 180^@/pi`

`(5pi)/8 "radians" =(5pi)/8*180^@/pi=(5cancelpi)/8*180^@/cancelpi=112.5^@`