If f(t) = csc (t) and f(a) = 2, find the exact value of:
(A) f(-a)
(B) f(a) + f(a + 2pi) + f(a + 4pi)
csc(t)=1/sin(t)
We know that sin(-t)=-sin(t) (you can check in on an unit circle)
And the sine function is periodic, that is sin(t+2k*pi)=sin(t), where k is any integer.
We know that sin(-t)=-sin(t) (you can check in on an unit circle)
And the sine function is periodic, that is sin(t+2k*pi)=sin(t), where k is any integer.
This is not a matter of knowing the periodic functions.
This is just plugging and chugging but I have no idea how to break it down.
This is not a matter of knowing the periodic functions.
This is just plugging and chugging but I have no idea how to break it down.
Why don't you try ?
I'm telling you that the sine function is periodic. That is to say, for example, $\displaystyle \sin(t+2 \pi)=\sin(t)$.
Thus $\displaystyle \csc(t+2 \pi)=\csc(t)$. This helps for question B.