[MOVED] trig review prob.: cos (x) * sin (x) - sin (x) = 0

[velocity]

cos (x) * sin (x) - sin (x) = 0

I added the sin (x),
Then I divided sin (x) from both sides and got cos (x) = 1,
I subtracted the 1 and am now at cos (x) - 1 = 0

What can I do now? Or did I go about it the wrong way? Thanks

 

[galactus]

You have it kicked.

Solve \(\displaystyle cos(x)=1\)

What values of x make cosine equal 1?

 

[velocity]

Only pi/2 is where cos(x) = 1

I don't know why I am always trying to make it so much harder than it is. Thanks

 

[skeeter]

'fraid not ...

cosx = 0 at x = pi/2

cosx = 1 at x = 0

 

[velocity]

i thought cosine was the y-coordinate?

 

[soroban]

Re: check this trig review problem?

Hello, velocity!

\(\displaystyle \cos x\cdot\sin x\,-\,\sin x \:= \:0\)

I added the sin (x)
Then I divided sin (x) from both sides and got cos (x) = 1 . . . . no

Factor: \(\displaystyle \:\sin x(\cos x\,-\,1)\:=\:0\)

We have: \(\displaystyle \:\sin x \,=\,0\;\;\Rightarrow\;\;x\,=\,0,\:\pi,\;2\pi,\;\cdots\)

. . . .and: \(\displaystyle \:\cos x\,-\,1\:=\:0\;\;\Rightarrow\;\;\cos x\,=\,1\;\;\Rightarrow\;\;x\:=\:0,\:2\pi,\:4\pi,\:\cdots\)


\(\displaystyle \text{Solution: }\,x\:=\:n\pi\;\text{ for any integer }n\)

 

[skeeter]

i thought cosine was the y-coordinate?

you thought wrong ...

in alphabetical order,
x comes before y & cosine comes before sine.