Question

trying to understand finding exact solutions on the interval 0, 2pi. when cos t= -.567? I know the answer is 2.17 but how do i find other possible exact answers?

Answer 1

so is there a positive and negative answer in radians?

Answer 2

but by taking the negative inverse of the cosine value (-.567) that's how I got the first result

Answer 3

well thats not quite right... as if you have you calculator in radian mode

find

cos(2.17)

what happens...?

Answer 4

i get -.5639

Answer 5

ok... so thats a 2nd quadrant angle... 2.17 radians...


the 3rd quadrant where cos is also negative is

\[\pi + 2.17 =\]

Answer 6

well that equals 5.31?

Answer 7

so check by finding

cos(5.31)

what do you get...?

Answer 8

.9957

Answer 9

ummm... somethings not right...

Answer 10

I just realised

so find the angle where cos(t) = .567

Answer 11

I'm not sure how to find that?

Answer 12

just inverse cos(0.567)

Answer 13

i get .9679?

Answer 14

great so t = 0.9679 radians

cos is negative in the 2nd and 3rd quadrants...

so

2nd quadrant use

\[\pi - t \]

3rd quadrant use

\[\pi + t\]

and you'll have your 2 angles...

Answer 15

so I have 2.17 & 4.11 but shouldn't the 4.11 be a negative?

Answer 16

the 2nd quadrant angle will be 2.17.... as you were able to get with the calculator

so to test the 3rd quadrant angle find

cos(4.11) and it should be -0.567

Answer 17

aaaahhh... ok. So how do you know when to add/subtract pi, or add/subtract 2pi?

Answer 18

yep... the method is

1 find the value of the positive

so find inverse cos(0.567)

that gives the angle

know the quadrants and which ratios are positive and negative..

then know

2nd quadrant angles are

\[\pi - \theta\]

3rd quadrant angles are

\[\pi + \theta\]

4th quadrant angles are

\[2\pi - \theta\]

hope it helps

Answer 19

oh. great. ty very much. I appreciate your help. It's much clearer now.