find the slope of the line passing through the origin and the line is perpendicular to the second line passing through the origin at an angle of (5pi)/8

Question

find the slope of the line passing through the origin and the line is perpendicular to the second line passing through the origin at an angle of (5pi)/8

Answer 1

Two ways to derive:

1.

The slope of the given line (5π/8) is (sin 5π/8) / (cos 5π/8).

Therefore the slope of the perpendicular is the negative reciprocal, (-cos 5π/8π) / sin 5π/8).

2.

The perpendicular line makes and angle of π/8 (5π/8 - π/2).

Therefore the slope of the perpendicular is (sin π/8) / (cos ππ/8)