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C2 maths help

man111111

Why does (sin 2x) / (cos 2x) = tan 2x . I thought the answer was tan x because the 2s cancel each other out

Reply 1

Apachai Hopachai

Original post by man111111

Why does (sin 2x) / (cos 2x) = tan 2x . I thought the answer was tan x because the 2s cancel each other out

nah, g math don't work like that.

\sin ()

is a function.

\cos()

is a function

You are applying

2x

to that function, you can't just cancel the (2x). Imagine the trig functions as vacuum cleaners, once you suck something up with the vacuum cleaner you can't get it back in it's purest form.

(edited 6 years ago)

Reply 2

storm95

if it was 2sin x and 2cos x you could've cancel the 2s out, ah man i do miss a level maths :')

Reply 3

Apachai Hopachai

As a more general formula

\frac{\sin()}{\cos()} = \tan()

So....

\frac{\sin(1)}{\cos(1)} = \tan(1)

\frac{\sin(x)}{\cos(x)} = \tan(x)

\frac{\sin(2x)}{\cos(2x)} = \tan(2x)

\frac{\sin(3x)}{\cos(3x)}= \tan(3x)

In words, Sine of anything, divided by cosine of that same anything equals tangent of that same anything

Have I left anything out? :wink:

nah that's moist :s-smilie:

(edited 6 years ago)

Reply 4

RDKGames

Study Forum Helper

Original post by Apachai Hopachai

As a more general formula

\frac{\sin()}{\cos()} = \tan()

So....

\frac{\sin(1)}{\cos(1)} = \tan(1)

\frac{\sin(x)}{\cos(x)} = \tan(x)

\frac{\sin(2x)}{\cos(2x)} = \tan(2x)

\frac{\sin(3x)}{\cos(3x)}= \tan(3x)

In words, Sine of anything, divided by cosine of that same anything equals tangent of that same anything

Have I left anything out? :wink:

nah that's moist :s-smilie:

That "anything" cannot equal

\frac{\pi}{2}+\pi n

for

n\in \mathbb{Z}

otherwise you get division by 0

Reply 5

Apachai Hopachai

Original post by RDKGames

That "anything" cannot equal

\frac{\pi}{2}+\pi n

for

n\in \mathbb{Z}

otherwise you get division by 0

yes

Reply 6

Virolite

Original post by RDKGames

That "anything" cannot equal

\frac{\pi}{2}+\pi n

for

n\in \mathbb{Z}

otherwise you get division by 0

you had to confuse it..

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