Question

can i write sin(11pi) as sin(pi) or even sin(0) ?

Answer 1

Sin(pi) and sin(11pi) have the same value, but neither of them are the same as sin(0). Sin is periodic, it has the same values every time you add any multiple of 2pi to a current spot. So sin(pi) is the same as sin(3pi) sin(5pi) sin(7pi) etc etc. Any value of sin wikll have the same value if you add or subtract multipl;es of 2pi. That is why sin(pi) and sin(11pi) are the same, but sin(0) is different from both.

Answer 2

Thank you very much, i was trying to figure out if sin(11pi) was undefined in
Dm(sin)=[-(2/pi);2/pi].

Answer 3

Yeah, you would just say itsthe same as sin(pi) and youd be cgood for that interval; :3

Answer 4

But isn't it then the complementary angle ? I have to figure out what arcsin(sin(11pi)) equals, i know i have to use identity cancellation, but since sin(11pi) is undefined in the defined interval for Sin(x), i have to 'rewrite' it as something thats within the defined interval for Sin. If i use the complementary angle would it still make sense ?
As in: sin(11pi)=sin(pi-0)=sin(0)
<=>
arcsin(sin(0))=0

Answer 5

Yes you can