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C2: Trigonometrical equations

Hi everyone, I’ve got a question 3tan⁡x+2cos⁡x=03 \tan x + 2 \cos x = 0 that I really don’t know what to do with! I’d be really grateful if someone could give me some pointers.

So I thought it would be the tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac {\sin \theta}{\cos \theta} identity that would be useful here. So I rearranged to
3sin⁡xcos⁡x+2cos⁡x=03 \frac {\sin x}{\cos x} + 2 \cos x = 0 but then after that my mind froze and I really didn’t know what to do! :confused:
Multiply each term by cos x. Now it is possible to form a quadratic equation in sin x.
Reply 2
Avatar for dslc
dslc
Original post by Mr M
Multiply each term by cos x. Now it is possible to form a quadratic equation in sin x.


Applying knowledge of cos2x+sin2x=1, additionally.
(edited 12 years ago)
Reply 3
Avatar for Crying Egg
Crying Egg
you are going the right way. after where you got upto youget (3sinx/cosx)+2cosx=0 therefore (3sinx/cosx)=-2cosx so then 3sinx = -2cos^2x you should know what cos^2x is equivalent to and then when you substitute that you get a quadratic equation and get two values for sin x and then solve them for their given ranges. i dunno if im doing this right because you havent given the answer but i got sinx = -0.5 or 2
Original post by dslc
Applying knowledge of cos2x+sin2x=1, additionally.


I bet you blurt out the punchlines to jokes too.
Reply 5
Avatar for dslc
dslc
Original post by Mr M
I bet you blurt out the punchlines to jokes too.


Well actually, what you said was wrong.

It wasn't possible to form a quadratic without applying the information I added.

Apologies if I stole a little of your TSR thunder though.
Original post by dslc
Well actually, what you said was wrong.

It wasn't possible to form a quadratic without applying the information I added.

Apologies if I stole a little of your TSR thunder though.


"The butler did it!"
Reply 7
Avatar for gavinlee
gavinlee
OP
Thanks everyone for your help - that's really cleared it up for me :biggrin:
Reply 8
Avatar for kingfisher
kingfisher
Original post by dslc
Applying knowledge of cos2x+sin2x=1, additionally.


Could please help me with some statistic concepts?
Reply 9
Avatar for dslc
dslc
Original post by kingfisher
Could please help me with some statistic concepts?


I can try and help you with some statistics concepts, yes.

Perhaps consider starting a new thread however, given that they'd be unrelated to trigonometrical equations.

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