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

In summary, to find the intersection of sin(x) and cos(x), you can set them equal to each other and solve for x. Alternatively, you can graph the equations and find the point of intersection. But if the problem involves sin(x) and cos(2x), you would need to use a half-angle formula to solve it. In this case, you can use the identity \tan ^2 x + 1 = \frac{1}{\sin ^2 x} to eliminate sin^2(x) and solve for x. However, if the problem involves 2sin(x)^2=tan(x), you would need to factor and use algebra to solve for x.
  • #1
expscv
241
0
how do i find intersection of sin(x) and cos(x)? wat method do i use?
 
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  • #2
sinx = cosx
sinx/cosx = 1
tanx = 1
x = arctan(1)
x = pi/4

cookiemonster
 
  • #3
expscv said:
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( :redface: ) has done
 
  • #4
but wat if is sin(x) and cos(2x) ?
 
  • #5
That's a little more difficult. You'd have to use a half-angle formula and solve it similarly.

cookiemonster
 
  • #6
with ur help it seems to be

[tex]sin(x)= 1- 2sin(x)^2[/tex]

[tex]2sin(x)^2+sin(x)-1=0[/tex]

hey it works thanks all
 
  • #7
wait but how do i solve 2sin(x)^2=tan(x)
 
  • #8
Use the identity:
[tex]\tan ^2 x + 1 = \frac{1}{\sin ^2 x}[/tex]
 
  • #9
omg i don't reallyget how this identity could help me~
 
  • #10
Eliminate the sin^2(x) with that identity.

cookiemonster
 
  • #11
That identity should give you:

[tex]4\sin ^6 x + \sin ^2 x - 1 = 0[/tex]

Now let t = sin2x and solve the equation.

(I eliminated tanx rather than sinx.)
 
  • #12
yeah but it trun out to be tan(x)^3+tan(x)-2=0
 
  • #13
So now you got to do some more factoring. More fun algebra!

Edit: Fine!

cookiemonster
 
Last edited:
  • #14
I think it's -2...
 
  • #15
god i m having a headache with everything
 
  • #16
thx all , i do this after i wake up tommor
 
  • #17
wait tan^2+1= 1/cos^2 is it?
 
  • #18
No, [itex]\tan ^2 x + 1 = \frac{1}{\sin ^2 x}[/itex].
 
  • #19
Chen, you might want to check that, as tan of 0 is not infinity.
 
  • #20
Of course you are right.

[tex]\tan ^2 x + 1 = \frac{1}{\cos ^2 x}[/tex]
 

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

What is the intersection of trig F(x)?

The intersection of trig F(x) refers to the points where the graph of the trigonometric function F(x) intersects with the x-axis.

Why is the intersection of trig F(x) important?

The intersection of trig F(x) is important because it helps us determine the solutions to trigonometric equations and can provide valuable information about the behavior of the function.

How do you find the intersection of trig F(x)?

To find the intersection of trig F(x), we set the function equal to zero and solve for the values of x that make the equation true. These values represent the x-coordinates of the points of intersection.

Can the intersection of trig F(x) be negative?

Yes, the intersection of trig F(x) can be negative. This occurs when the function crosses the x-axis below the origin, resulting in negative x-coordinates for the points of intersection.

Are there any special cases for the intersection of trig F(x)?

Yes, there are special cases for the intersection of trig F(x) when dealing with periodic functions, such as sine and cosine. In these cases, there may be an infinite number of points of intersection due to the repeating nature of the functions.

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