plane trig

[jhawatmeh]

sinθ= −√3 /2 and θ in QIII.

I got theta = 210 degrees, what am I doing wrong?

 

[Deleted member 4993]

sinθ= −√3 /2 and θ in QIII.

I got theta = 210 degrees, what am I doing wrong?

How do you know that you were doing something wrong?

If you want us to catch your mistake - you would need to share your work.

 

[The Highlander]

sinθ= −√3 /2 and θ in QIII.

I got theta = 210 degrees, what am I doing wrong?

This may help (if you study it carefully):-
(NB: Within the brackets, the first value is the Cosine and the second is the Sine!)

{img]https://i.ibb.co/74hk5sF/Exact-Values-Chart-Unit-Circle.png[/img]
(For ease of replication should anyone wish to reproduce it. Just remember to replace the leading "{" with "[")​

 

[The Highlander]

sinθ= −√3 /2 and θ in QIII.

I got theta = 210 degrees, what am I doing wrong?

Dear @jhawatmeh,

I would “guess” from your post that you are at a stage in your Mathematical learning where you are being introduced to (or have already been taught) about the Exact Values of the Trigonometric Ratios for 30°, 45° & 60°.
To make any positive progress in the topic of Trigonometry you need to know these values or at least be able to derive them from first principles; they are very important and crop up repeatedly in the topic.
I have inserted, below, a copy of a Worksheet and I urge you to make your own copy of it and fill in all the blanks yourself.
You should retain a completed copy of this Worksheet in all your workbooks unless or until you are confident that you know all the results (or can derive them from the first principles provided in the worksheet) without further reference to it.
However, the Worksheet only provides the Exact Values for those angles in the first Quadrant. The numerical values of the ratios will remain the same regardless of which quadrant these (referred) angles (eg: 210° ≡ 180° + 30°) are in but, of course, their signs will be affected (based on the acronym: ASTC, with which I trust you are familiar.)
It will be of little benefit to you if you simply ‘read off’ the correct answer from the Exact Values “Chart” that I provided for you in my previous post which is why I decided to take the time to offer this further advice.
I do hope that you will take it on board and make the effort to assimilate the knowledge I am guiding you towards.
It would also be gratifying if you were to respond showing how you have now approached your problem and, perhaps, reached an ‘alternative’ answer using the information I have provided for you.

How to Derive the Exact Values of the Sine, Cosine & Tangent of 30, 45 & 60 degrees:-

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