What are the zeros of the function f(x)=sinx+cosx found in interval (0,pi)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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