Question

Find all values of theta between 0 and 360 that satisfy cos(theta)=-.73

Answer 1

better get started.

Answer 2

just start plugging in numbers. go from 0 to 360

Answer 3

yes, that's the first step

Answer 4

what do you get?

Answer 5

you get 136.8863941

Answer 6

and then quadrants 2 are 3 are the only valid ones because they have negative cosines

Answer 7

but how do i reflect the angle from the 3rd quadrant to the second

Answer 8

look at a diagram of a sine, and a cosine wave

value (degrees) 0-90......... 90-180........180-270...... 270-360
sine wave.........positive ... positive ........ negative... negative
cosine............. positive.... negative ....... negative ... positive

so,
if cos is a neg value, that puts it between 90 - 270 (second and third quadrant)

if sine is neg that puts it between 180 - 360 (third and fourth quadrant)

just find the values for cos = - 1/2 and you will have 2 values one in the second quadrant, and one in the third

Answer 9

i know that, i have one in the third, but how do i find one in the second? thanks.

Answer 10

Subtract the reference angle from 180

Answer 11

http://www.wolframalpha.com/input/?i=arccos%28-.73%29

Answer 12

then other one is 360 minus the first one