Question

Help with Trig--
sin X + 2 sin X cos X= 0
solve for all possible radian solutions
(please explain each step) Thank you

Answer 1

do you know your trig identities?

Answer 2

yes, 2 sin x cos x = sin 2A

Answer 3

good, then when does

sin(x) + sin(2x) = 0?

recall also that " -sin(x) = sin(-x)" that might be useful

Answer 4

sin(2x) = -sin(x)

sin(2x) = sin(-x)

2x = -x

2x + x = 0

3x = 0 .... when x = 0

thats what I come up with as a solution....

Answer 5

0 and pi i believe are the answers

Answer 6

thats what I got as an answer, but the answers in the back of the textbook says differently : pi k, 2 pi/3 +2 pi k, 4 pi/3 +2pi k

Answer 7

ahhh.... ALL possible solutions involves an interger constant of "k"

Answer 8

there do appear to be 3 spots between 0 and 2pi that match up...

Answer 9

ohhhh

Answer 10

i see it, but i dont understand

Answer 11

how to get the points without knowing it

Answer 12

...yeah, trig is highly visual.

Answer 13

we could try this:

sin(x) + 2 sin(x) cos(x)= 0

sin(x)(1 + 2cos(x)) = 0

Answer 14

sin(x) = 0 is a solution

and (1+2cos(x)) = 0 are solutions

Answer 15

1+ 2 cos(x) = 0

2cos(x) = -1

cos(x) = -1/2

Answer 16

that works better :)

Answer 17

0, pi for sin(x)

cos(x) is negative in Q2 and Q3...

Answer 18

cos(pi/3) = 1/2 .... 60 degrees.

that would make it 120 degrees and 240 degrees as well.

Answer 19

2pi/3 + k2pi and 4pi/3 + k2pi...right?

Answer 20

yes, thank you very much!... I can see a light at the end of the tunnel!!! thank you

Answer 21

:) all it takes is a little persistents and alot of luck lol

Answer 22

thank you, your right about that!!