Find the slope of a line

Question

Find the slope of the line passing through the origin, which is perpendicular to a second line, l, passing through the origin at an angle of 5pi/9. Round to 3 decimal places

Answer 1

the line through the origin with angle = 5pi/9 has slope = tan(5pi/9)

pi/3 = 60

pi/9 = 20

5pi/9 = 100

tan100 =about -5.67128

a perpendicular line would have slope = the negative inverse = -1/tan100 = -cot100

y= exactly -cot(100)x

or

y = -cot(5pi/2)x

or

y = about 0.17632698x is the equation of the perpendicular line through the origin

it may help to draw a rough sketch of the graph of the two lines

the first line is downward sloping with fairly steep slope, close to vertical, close to the y axis

the perpendicular line is upward sloping, close to horizontal, close to the x axis