I need to find sin(4a) if tga=3/4 what I do:

$$\sin(4a)=2\sin(2a)\cos(2a)$$
$$tg=\frac{ sina }{ cosa }$$

Question

I need to find sin(4a) if tga=3/4 what I do: 

$$\sin(4a)=2\sin(2a)\cos(2a)$$
$$tg=\frac{ sina }{ cosa }$$

kamille · Answer

can you help me @arifadli8

anonymous · Answer

sorry i cant help u

anonymous · Answer

hint... does it look like a 3-4-5 triangle to anyone?

anonymous · Answer

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if not, follow hartnn's steps

kamille · Answer

shouldnt be included*

kamille · Answer

I have never learnt about sec at school, so I think it shouldnt be included in finding the answer. Any other tips?

anonymous · Answer

not needed.. 
tangent is opp side / adj side
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anonymous · Answer

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no need.
you know that tangent = opp side / adj side

kamille · Answer

yes

anonymous · Answer

and find the third side, the hypotensuse.. (Pythagorean them)
then,
sin = opp side / hypotenuse.

anonymous · Answer

so, you'd get opp side = 3
adj side = 3
hyp = 5

anonymous · Answer

now, keep splitting sin(4A) till you get it in terms of sin(A) and cos(A)

kamille · Answer

but, actually, it is not true. Where from you find it is 3 and 4? : ) it also can be 12 and 9

anonymous · Answer

as long as you maintain the (3/4) ratio, you are good :)

anonymous · Answer

keeping things simple will always help

kamille · Answer

well, wont it change sin value?

kamille · Answer

and also, I have forrgoten to say pi<a<3/2pi

anonymous · Answer

nope.. the ratio you'd get is still the same..
when you scale the ratio, only the "size" of triangle i.e., the sides change but the angles and ratios do not

The golden rule of trigonometry

anonymous · Answer

aha...
now... things are a bit differet

kamille · Answer

well, I am still not sure if it is a rational way to do it. Because we can't say what we don't have.

anonymous · Answer

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