Question

I'm trying to solve this but I honestly have no idea how to move forward. All I have done so far is this:

theta=tan^-1(-1)

Now I'm stuck <_>

Answer 1

@greysmither what's tan 45?

Answer 2

it is 135 degree ,, Aren't u allowed to use calculator??

Answer 3

Avva 135 is just one of the answer, it has several answers

Answer 4

tan-1 only has one answer :)

Answer 5

@amistre64 tan (theta)=-1 will have several solutions

Answer 6

yep

Answer 7

yup you can add 180 degrees and you'll figure out that 135 n 315 both have tan of -1

Answer 8

\[\tan \theta=-1\]
so
\[\theta = n\pi +3\frac{\pi}{4}\]
n=0, 1, 2, 3 and so on

Answer 9

So this pretty much a unit circle-dependent problem?

Answer 10

this is*

Answer 11

Yeah:)

Answer 12

Could it also be \[7\pi/4 + \pi n\]?

Answer 13

since both of those quadrants create -1?

Answer 14

Yeah it should be
\[ n\pi \pm \pi/4\]
n=1,2 ,3 and so on
I missed that, it'd include \(7\pi/4 + n\pi\) also

Answer 15

I thought that you couldn't include pi/4 and 5pi/4 in quadrants 1 and 3 because they equal 1 when I'm looking for -1?

Answer 16

So confusing :(

Answer 17

Sorry, Just wait for some time, I'll help you:)

Answer 18

Sorry kept you waiting:(

Answer 19

Its okay I really appreciate your help

Answer 20

We have
\[\tan x=-1\]
so x is eithere 3pi/4 , 7pi/4 and so on
\[x= n\pi -\pi/4\]
if n=1
x=3 pi/4
n=2
x= 7 pi/4
so this will include all possible solutions. This is your answer

Answer 21

So, just to clarify \[x=-\pi/4+n \pi\] is the final answer.
I can't thank you enough!! I wish I could give you 100 medals ;)

Answer 22

Thanks Greysmither , this is the answer:)