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.