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Mathematics 46 Online
OpenStudy (anonymous):

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

OpenStudy (amistre64):

do you know your trig identities?

OpenStudy (anonymous):

yes, 2 sin x cos x = sin 2A

OpenStudy (amistre64):

good, then when does sin(x) + sin(2x) = 0? recall also that " -sin(x) = sin(-x)" that might be useful

OpenStudy (amistre64):

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....

OpenStudy (amistre64):

0 and pi i believe are the answers

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

ohhhh

OpenStudy (anonymous):

i see it, but i dont understand

OpenStudy (anonymous):

how to get the points without knowing it

OpenStudy (amistre64):

...yeah, trig is highly visual.

OpenStudy (amistre64):

we could try this: sin(x) + 2 sin(x) cos(x)= 0 sin(x)(1 + 2cos(x)) = 0

OpenStudy (amistre64):

sin(x) = 0 is a solution and (1+2cos(x)) = 0 are solutions

OpenStudy (amistre64):

1+ 2 cos(x) = 0 2cos(x) = -1 cos(x) = -1/2

OpenStudy (amistre64):

that works better :)

OpenStudy (amistre64):

0, pi for sin(x) cos(x) is negative in Q2 and Q3...

OpenStudy (amistre64):

cos(pi/3) = 1/2 .... 60 degrees. that would make it 120 degrees and 240 degrees as well.

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

thank you, your right about that!!

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