Question

3SIN2THETA - 2SINTHEA = 0

Answer 1

is it this problem???: \(\large 3sin^2\theta - 2sin\theta = 0 \)

Answer 2

3sin2theta - 2sintheta

Answer 3

NO exponents in the first part.

Answer 4

\(\large 3sin(2\theta)-2sin\theta=0 \) like this?

Answer 5

yeah

Answer 6

ok...
use the double angle formula for sine...: \(\sin(2\theta) = 2sin\theta cos\theta \)

Answer 7

replace that into your original equation... what you got now?

Answer 8

\[\huge 3\color {red}{sin(2\theta)}-2sin\theta=0 \]
\[\huge 3\color {red}{2sin\theta \cdot cos\theta}-2sin\theta=0 \]

Answer 9

6sintheta(costheta) - 2sintheta =0

Answer 10

yep....
now factor out a sin(theta)..... from the left side...

Answer 11

sintheta (6costheta - 2) = 0

Answer 12

great....
now just set each factor equal to zero and solve....

Answer 13

okay thanks!

Answer 14

solve both:
\(\large sin\theta = 0 \) and \(\large 6cos\theta - 2=0 \)

Answer 15

are you looking for the general solution or solutions within [0, 2pi) ????

Answer 16

solutions like Pi 2Pi

Answer 17

so the general solution...????

Answer 18

okay

Answer 19

from that fist equation, \(\sin\theta=0 \)---> \(\theta=n\cdot \pi \), where n is an integer....

Answer 20

okay

Answer 21

from the second eqaution, \(\large 6 cos\theta - 2=0 \rightarrow cos\theta=\frac{1}{3} \)
so \(\large \theta=Arccos\frac{1}{3} + \)

Answer 22

Arc cos 1/3 +?