SOLUTION: What is the solution when solving tan theta= - square root 2 sin theta

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Question 1095722: What is the solution when solving tan theta= - square root 2 sin theta
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
The solutions are   theta = 0 degrees  or  theta = 180 degrees. 


There are NO other solutions in the interval  0 <= theta < 360 degs.


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Yes, I really missed that roots. Sorry.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

Tutor ikleyn's answers are usually reliable; but she missed something here. Since she didn't show any work in her response to your question, I don't know how she arrived at her incorrect answer.

tanx+=+-sqrt%282%29%2Asinx
sinx%2Fcosx+%2B+sqrt%282%29%2Asinx+=+0
sinx%281%2Fcosx%2Bsqrt%282%29%29+=+0
sinx=0 or 1%2Fcosx=-sqrt%282%29

sinx=0 gives x=0 and x=pi, as shown in ikleyn's response.

1%2Fcosx=-sqrt%282%29 gives the two additional solutions x+=+3pi%2F4 and 5pi%2F4

Graphing the two expressions with a graphing calculator confirms the four solutions.