Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer):
7 cos θ sin θ + 2 cos θ = 0

Answer 1

I tried it and got \[\theta=\frac{ \Pi }{ 2 } and \frac{ 3\Pi }{ 2 }\] ...but its wrong

Answer 2

First factor out the cos theta:

\[\cos(\theta)(7\sin(\theta) + 2) =0\]

\[\rightarrow \cos \theta =0 \]

or

\[7\sin(\theta) + 2 = 0\]

Jut solve those two.

Answer 3

yeah, that's what I did and since the second one you cant find the sine of -2/7 I can't solve for that one.
Which leaves only pi/2 and 3pi/2 for the first one.

Answer 4

you can find sin(x) = 2/7

then use the angles in any quadrant to fin the solution

sin is negative in the 3rd (pi + x) and 4th quadrant (2pi - x)

this will allow you to find all the solutions.