trig equation: find value of x in cos(3x)= -0.419 for 0<x<

[zack]

find the value of x
cos(3x)= -0.419 for 0<x<270

I do arc cos -0.419 which equals 114.77

and then to find the second angle in the 3rd quadrant

why do I need to minus 360 to get the degree in the 3rd quadrant?

why not add 90 to 114.77 to make it in the 3rd quadrant?

someone please explain this

[little_dragon]

find the value of x
cos(3x)= -0.419 for 0<x<270

I do arc cos -0.419 which equals 114.77

and then to find the second angle in the 3rd quadrant

why do I need to minus 360 to get the degree in the 3rd quadrant?

why not add 90 to 114.77 to make it in the 3rd quadrant?

look @ the graph
the 1st one is 0+114.77 (114.77 in from the left)
the 2nd one is 360-114.77 (114.77 back from the right)
doing +90 doesnt work w/ the graph fo what cos does