Question

No idea how to solve this: Find all solutions if
0 ≤ x < 2π.
Use exact values only. (Enter your answers as a comma-separated list.)
sin x cos 2x + cos x sin 2x = 1/2

Answer 1

\[\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)\]

Answer 2

that's a hint

Answer 3

3x=1/2 but where do i go from there

Answer 4

you mean sin(3x)=1/2

Answer 5

yes

Answer 6

\[0 \le x < 2\pi \\ \text{ let } u=3x \\ \text{ so } \frac{u}{3}=x \\ 0 \le x < 2\pi \text{ implies } 0 \le \frac{u}{3} < 2\pi \\ \text{ so solve } \sin(u)=\frac{1}{2} \text{ on } 0 \le u < 6 \pi \\ \text{ then after you are done replace u with 3x and solve for x}\]

Answer 7

i have no idea what you are saying

Answer 8

sin(u)=1/2 can be solved on [0,6pi) using the unit circle

Answer 9

ohhhh

Answer 10

soooo