Equating two functions to find value of x ?

Question

y=sinx , y= (2/pi)x 

 

What is the process of doing this ?

Answer 1

Hello Alex,

 

Try plotting the graphs by hand. You'll discover three distinct intersection points. Furthermore, as long as you were careful with your plot, you'll be able to read off the exact coordinates of all three intersection points.

 

Apart from plotting the functions and seeing where they intersect, there's no analytical method for solving this equation. You'd need to resort to estimations and guesswork (like using a series expansion approximation for sin(x), for example).

 

There's also another way to find all possible solutions for this problem, but it requires a very good understanding of what y = sin(x) looks like, the properties of even/odd functions, and the concept of a trivial solution. But... if you're already familiar with these things, then doing the graphs should be a piece of cake.

Answer 2

A good way to solve this would be on the graphing calculator; put it into RADIAN mode, then define Y1 & yY as indicated above, then set the window reasonably (say x interval [-pi/2, pi/2] and y interval [-1,1]).

 

Then use the CALC Intersect feature.