# Intersection of trig F(x)

1. Apr 11, 2004

### expscv

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

2. Apr 11, 2004

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

3. Apr 11, 2004

### himanshu121

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

4. Apr 11, 2004

### expscv

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

5. Apr 11, 2004

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

6. Apr 11, 2004

### expscv

with ur help it seems to be

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

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

hey it works thx all

7. Apr 11, 2004

### expscv

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

8. Apr 11, 2004

### Chen

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

9. Apr 11, 2004

### expscv

omg i dont reallyget how this identity could help me~

10. Apr 11, 2004

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

11. Apr 11, 2004

### 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.)

12. Apr 11, 2004

### expscv

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

13. Apr 11, 2004

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

Edit: Fine!

Last edited: Apr 11, 2004
14. Apr 11, 2004

### Chen

I think it's -2...

15. Apr 11, 2004

### expscv

god i m having a headache with everything

16. Apr 11, 2004

### expscv

thx all , i do this after i wake up tommor

17. Apr 11, 2004

### expscv

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

18. Apr 11, 2004

### Chen

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

19. Apr 11, 2004

### matt grime

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

20. Apr 11, 2004

### Chen

Of course you are right.

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