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So I have been asked this question:

Suppose $$\theta = 0.5\pi + \sin(\theta).$$Verify by calculation that $\theta$ lies between $2.2$ and $2.4.$

What my book has done is put all the terms on the left-hand site and replace the $0$ on the right-hand side with $f(\theta)$.

My question is, why am I not asked to find the root of $\theta$? Why am I asked to find $\theta$? And from the function what happens with the $0$?

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1 Answer

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"Roots" refer to the values that make a polynomial equal to zero. For example, if $p(x)=x^2-2x+1$ is your polynomial, then to find the roots you set up the equation $x^2-2x+1=0$ and find values of $x$ that solve it.

If you have a pre-existing equation, you don't call solutions to it "roots."

Roots of polynomials are important because they have to do with factoring. In the above polynomial, $x=1$ is a root, and with some more work we can factor it as $(x-1)^2$.

(Note: it's reasonably common to talk about roots of a function as well, but at least in my experience it's more common for non-polynomial functions to call them "zeros.")

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