Question

Solve: sin3Ө = 0

Answer 1

arcsin

Answer 2

sin3Ө = sin 0

Answer 3

--> Ө = 0

Answer 4

i don't get it -.-

Answer 5

Sin 0 =0. 0*any number is 0, so theta would be 0 because 0*3=0

Answer 6

Ok?

Answer 7

0 is not the only solution

Answer 8

Really?

Answer 9

sin(180º)=0...right? sin(360º)=0, sin(-180º)=0

Answer 10

Okk then ?

Answer 11

you have to account for every angle

Answer 12

what is 120 degrees k mean ?

Answer 13

what is "k" anyway ?

Answer 14

k is an integer, any integer

Answer 15

which is how you account for every possible angle theta can be

Answer 16

how did they get 120 degrees k then ?

Answer 17

the answer to this is theta=k*60º, where k is any integer

Answer 18

for example
k=1 sin(3*60)=sin(180)=0
k=0 sin(3*0)=sin(0)=0
k=-1 sin(3*-60)=0
k=2 sin(3*2*60)=sin(360)=0

Answer 19

ohh

Answer 20

where did you get the 60 from?

Answer 21

well you could also write 0+k*60º, since we established that the reference angle was 0, but the 0 is unnecessary

Answer 22

so k= either 0,1,2,3 ?

Answer 23

k is ANY integer

Answer 24

the equation will be true whatever the value you plug in for k is

Answer 25

i see

Answer 26

suppose k=500
type in your calculator sin(3*500*60º)
you end up with 0

Answer 27

ahh ok

Answer 28

Sin and cos have periodic of 2 pi
=> sin 3Ө = sin 0 + k 2pi
=> 3Ө = 0 + k 2pi
=> Ө = k 2pi / 3 = k 60 degree
k = 1, Ө = 60
k = 2, Ө = 120
...
so on