Question

3 sin(x-pi/5) =0

Answer 1

using the sum and difference identities i get
0=3sin(x-pi/5)=\[3\sin(x)\cos(\pi/5)-3\cos(x)\sin(\pi/5)\]

Answer 2

solve for cos(pi/5) and sin(pi/5) in your calculator., and you may be able to figure it out from there.

Answer 3

x is pi/5 though...?? i think because 3sin(pi/5-pi/5)=0

Answer 4

are the answers supposed to be between 0 and 2pi?

Answer 5

ok so then if pi/5 is our reference angle and x has to be positive since were subtracting pi/5, in each of the we have to find the reference angle in quadrants 1 and 2 we have x=pi/5 x= pi-pi/5=4pi/5

Answer 6

but 3sin(pi) also = 0. so 6pi/5 - pi/5 = pi

Answer 7

\[3\sin \frac{ x-\pi }{ 5 }=0\]
\[\sin \frac{ x-\pi }{ 5 }=0\]
\[put \frac{ x-\pi }{ 5 } = t\]
\[\sin t = 0\]
\[t=0, \pi, 2\pi...... \]
\[\frac{ x-\pi }{ 5 }=0, \pi , 2\pi......\]
\[x-\pi=0,5\pi,10\pi.....\]
\[0 \le x \le2\pi , x=\pi\]