Trouble with C2 trig

I just don't get how to do these:
5sin2x=2cos2x, 0</x</=360

The furthest I can reach is tanx=2/5 so x=21.8 and that's all.

I just don't get how to do these:
5sin2x=2cos2x, 0</x</=360

The furthest I can reach is tanx=2/5 so x=21.8 and that's all.

I don't know what to do next.
Hulp somebody plz.

Have you been taught the CAST diagram?


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That is incorrect Tan2x =2/5

Be careful here - you mean tan(2x) = 2/5 don't you?

it should be tan2x not tanx

I meant tan2x, typo, sorry, but that is off point. The point is: how to proceed?
Yes, I know the CAST diagram, and I tried doing it that way (marking in 21.8 deg, taking half of that, adding 360 to it, etc) and it does not give me the correct answers.

you don't have to do the cast diagram... i find it unhelpful ?

instead for tan you add on multiples of 180 degrees to your first result ( which is for tan2x ). then divide by 2.

you don't have to do the cast diagram... i find it unhelpful ?

instead for tan you add on multiples of 180 degrees to your first result ( which is for tan2x ). then divide by 2.

You realise that is what the CAST diagram says

The methods (rule/CAST/graph) are all the same method - just presented differently

That is because you have to add values to the 2x before dividing by 2

Also, you should know that the Tan function repeats every 180

Yeah, I find it grossly unhelpful too.
And yeah, I've heard about adding multiples before, but what multiples? And then divide exactly what by 2?

Yeah, I find it grossly unhelpful too.
And yeah, I've heard about adding multiples before, but what multiples? And then divide exactly what by 2?

I do know it repeats every 180 deg, I just don't get how that'll help. Am I supposed to add 180 to 21.8 and then divide that by 2 or something? Idgi.

just use 1,2,3,4, multiples of 180 for tan
1,2,3,4 multiples of 360 for sin and cos.

Okay, so I'll add multiples of 180 to 21.8, fine. BUT there are millions of multiples of 180. I can't keep adding forever. I don't understand this.

Okay, so I'll add multiples of 180 to 21.8, fine. BUT there are millions of multiples of 180. I can't keep adding forever. I don't understand this.