How Do I Find the Intersection of \sin(x) and \cos(x)?

[expscv]

how do i find intersection of sin(x) and cos(x)? wat method do i use?

 

[cookiemonster]

sinx = cosx
sinx/cosx = 1
tanx = 1
x = arctan(1)
x = pi/4

cookiemonster

 

[himanshu121]

how do i find intersection of sin(x) and cos(x)? wat method do i use?

Apart from it u can do it graphically. But Still u have to do wat cookie monster( ) has done

 

[expscv]

but wat if is sin(x) and cos(2x) ?

 

[cookiemonster]

That's a little more difficult. You'd have to use a half-angle formula and solve it similarly.

cookiemonster

 

[expscv]

with ur help it seems to be

$$sin(x)= 1- 2sin(x)^2$$

$$2sin(x)^2+sin(x)-1=0$$

hey it works thanks all

 

[expscv]

wait but how do i solve 2sin(x)^2=tan(x)

 

[Chen]

Use the identity:
$$\tan ^2 x + 1 = \frac{1}{\sin ^2 x}$$

 

[expscv]

omg i don't reallyget how this identity could help me~

 

[cookiemonster]

Eliminate the sin^2(x) with that identity.

cookiemonster

 

[Chen]

That identity should give you:

$$4\sin ^6 x + \sin ^2 x - 1 = 0$$

Now let t = sin²x and solve the equation.

(I eliminated tanx rather than sinx.)

 

[expscv]

yeah but it trun out to be tan(x)^3+tan(x)-2=0

 

[cookiemonster]

So now you got to do some more factoring. More fun algebra!

Edit: Fine!

cookiemonster

 

[Chen]

I think it's -2...

 

[expscv]

god i m having a headache with everything

 

[expscv]

thx all , i do this after i wake up tommor

 

[expscv]

wait tan^2+1= 1/cos^2 is it?

 

[Chen]

No, $\tan ^2 x + 1 = \frac{1}{\sin ^2 x}$.

 

[matt grime]

Chen, you might want to check that, as tan of 0 is not infinity.

 

[Chen]

Of course you are right.

$$\tan ^2 x + 1 = \frac{1}{\cos ^2 x}$$