What are the zeros of the function f(x)=sinx+cosx found in interval (0,pi)?
We have to find the zeros of f(x) = sin x + cos x
f(x) = sin x + cos x = 0
=> sin x = -cos x
=> tan x = -1
x = arc tan (-1)
In the interval (0, pi) , x = -pi/4 + pi = 3*pi/4
The required value is x = 3*pi/4
First, we'll put sinx+cosx = 0.
We'll divide by cos x:
sin x/cos x + 1 = 0
We know that sinx/cosx=tan x
tanx + 1 = 0
tan x = -1
x = arctan(-1)
x = -arctan 1
Interval(0,pi) covers boths quadrants, 1st and the 2nd.
The tangent function has positive values in the 1st quadrant and negative values in the 2nd quadrant.
x = pi - pi/4 = 3pi/4
The solution of the equation is x = 3pi/4.