[Math] Correct answer of the following math related to Bisection Method.

Question

Use the Bisection method to find $p_3$ for $$f(x)=\sqrt x-\cos(x)$$ on $[0,1]$

I have got the answer $p_3=0.875$

But in answer script , $p_3=0.625$

Which one is correct?

let $[a,b]=[0,1]$

$f(a)=f(0)=-1$

$f(b)=f(1)=0.0001523$

so the root lies in [0,1]

$p_1=\frac{0+1}{2}=0.5$

$f(p_1)=f(0.5)=\sqrt {0.5}-\cos(0.5)=-0.292855141$

so the new interval is [0.5,1]

$p_2=\frac{0.5+1}{2}=0.75$

$f(p_2)=f(0.75)=\sqrt {0.75}-\cos(0.75)=-0.133888923$

so the new interval is [0.75,1]

$p_3=\frac{0.75+1}{2}=0.875$

Where is the mistake?

Answer 1

Your calculator is in degree mode. Switch it to radian mode.