Question

tan theta = tan theta ( 2 + sin theta)

Answer 1

Start by dividing both sides by tan theta

Answer 2

This will give you 1 = 2+sin theta

Answer 3

=> sin theta = -1

Answer 4

oh I feel stupid, thank you!!

Answer 5

hmm apparently that is not right

Answer 6

I need 2 different values and -90 is not one of them...

Answer 7

actually 90 might be I think but I need another value ?!?!

Answer 8

(another solution is tan theta =0)

Answer 9

please show me the working

Answer 10

Can you read this yet? \(tan \theta = tan\theta(2+sin\theta)\)

Answer 11

ye si can

Answer 12

its 3 sin theta btw

Answer 13

sorry I missed that out earlier

Answer 14

oh woops that might be why it is wrong..

Answer 15

ok I got 2 of the right answers now, jus need what tan= ...

Answer 16

Awesome!
expand terms
\[tan \theta = 2tan\theta + tan\theta sin\theta \]
Move everything to the right hand side\[tan \theta-2tan \theta-tan \theta sin\theta=0\]
Factor out tan\[tan \theta(1-2-sin\theta)=0 \]
From here we can say that either \(tan \theta=0\) or \(-1-sin\theta=0\)

Answer 17

Hope that makes sense!

Answer 18

Ok well 3 sin theta will simply change the final bit to something like \[-1-3sin\theta = 0\]For that solution, so no wozza!

Answer 19

hmm but the answers for tan should b 180 and 360, ...

Answer 20

I have noo Idea why :(

Answer 21

If you look at the graph of tan we can see that it repeats every 180 degrees. So actually when one writes \[tan^{-1}(0)\] it is more accurately equal to \(180n\) where n is any integer. So it could be 0, 180, 360, 540,720 etc. (and the same the other way. It helps to have a look at what the function looks like graphically. http://intmstat.com/trigonometric-graphs/tanx.gif

Answer 22

We are trying to find the points where it intersects the x axis. It is clear to see that there will be infinitely many points. For school question they generally just want you to find a couple between -360<x<360

Answer 23

Does that make sense? (Bit of information overload.)

Answer 24

hmm but we got tan theta= 1 or 3 sin theta when I put in 1 it gave 45 degrees. But the answers are 180 and 360. Wht have I done wrong?

Answer 25

I'm pretty sure we got \[tan\theta = 0 \]if you look up to my answer before.

Answer 26

yes we got 0, 1 and the sin one. How do you know which to use?

Answer 27

Because we had\[tan\theta (-1-3sin\theta)=0\] meaning that either \[tan\theta=0\]OR\[ -1-3sin\theta=0\]
I'm not sure where we got tan theta = 1 from ?

Answer 28

becaue usually when x is in brackets you just do +1 and + sin theta

Answer 29

oh I get it now thanks!!!!!!!!!!!!!!!!!!!!! you were great

Answer 30

Alright, good job! Sorry for not being clearer