I got stuck on solving the following equation. I try all the identities, but hopeless. Do you have any suggestion?
$(3x + \sin x) \cos x = -3, \quad\pi/2 \leq x \leq \pi$ Solve for $x$.
Please don't tell me to use the calculator!
I got stuck on solving the following equation. I try all the identities, but hopeless. Do you have any suggestion?
$(3x + \sin x) \cos x = -3, \quad\pi/2 \leq x \leq \pi$ Solve for $x$.
Please don't tell me to use the calculator!
I do not believe there is a closed form for this. You can only revert to numerical solutions, which are gotten from graphing the equation. One way to simplify the original is:
$3x \cos x + \sin x \cos x = -3$
Multiplying both sides by 2 leaves us with: $6x \cos x + 2\sin x \cos x = -6$
Then you could note $\sin 2x = 2 \sin x \cos x$ to get to: $6x \cos x + \sin 2x = -6$
From here, I would just plug in a few points and graph it to find a solution if I was told not to use a calculator.