Question

\[x={3 \over 4}\pi-\sin x\]The equation has one root. Verify by calculation that the root lies between 1.3 and1.5.

Answer 1

can you just say f(x) = (3/4)pi - sinx - x and find f(1.3) and f(1.5). if the signs are different then a root must exist between x=1.3 and x=1.5

Answer 2

What do you mean if the signs are different?

Answer 3

Oh, I understand. Don't worry. Thank you!

Answer 4

if f(1.3) is, say, positive, and f(1.5) is negative then that proves there must be a root between these two x values.