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# C2 small trig question watch

1. "It is given that 5sin3x = 2cos3x, what is tan3x equal to"

Im sure its something to do witht he fact that tan x = sinx/cosx but i dont know what to do from there.

If I let 3x = z then:

(5/2)tan z = 5sin z / 2cos z

... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
2. tan3x = sin3x/cos3x

Does that help at all?

EDIT: If you let 3x=z then:
5sinz=2cosz

divide both sides by cosz:
5sinz/cosz = 2

Now divide both sides by 5:
sinz/cosz = 2/5
3. tan3x = sin3x/cos3x
4. 5sin3x = 2cos3x
5/2 = sin3x/cos3x
5/2 = tan3x
x = (tan^-1 (5/2))/3

tap it into a calculator to see if it works..
5. (Original post by Slick168)
5sin3x = 2cos3x
5/2 = sin3x/cos3x
5/2 = tan3x
x = (tan^-1 (5/2))/3

tap it into a calculator to see if it works..
That's not right.
7. (Original post by dealer91)
"It is given that 5sin3x = 2cos3x, what is tan3x equal to"

Im sure its something to do witht he fact that tan x = sinx/cosx but i dont know what to do from there.

If I let 3x = z then:

(5/2)tan z = 5sin z / 2cos z

... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
5sin3x = 2cos3x

divide through by cos(3x)

5(sin(3x)/cos(3x))=2

then divide by 5, and as sin(3x)/cos(3x) = tan(3x) you get

tan(3x) = 2/5

is that what u wanted??
8. (Original post by dealer91)
... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
You know 5/2 tan z = 5sinz/2cosz.

Now look at the original equation and try and see what 5sinz/2cosz must be.
9. (Original post by dealer91)
"It is given that 5sin3x = 2cos3x, what is tan3x equal to"

Im sure its something to do witht he fact that tan x = sinx/cosx but i dont know what to do from there.

If I let 3x = z then:

(5/2)tan z = 5sin z / 2cos z

... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.

10. Ah yeah I see iot now thanks
11. ... that was BASIC ALGEBRA!!! what are they teaching you kids nowadays. hehe i htink i got confused with tryign to write it out correctly lolx

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Updated: April 15, 2008
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