# Find Exact Value

• Aug 22nd 2008, 02:32 AM
magentarita
Find Exact Value
Let t = theta for short

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)
• Aug 22nd 2008, 02:38 AM
Moo
Hello,
Quote:

Originally Posted by magentarita
Let t = theta for short

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.
• Aug 22nd 2008, 05:24 AM
magentarita
no...
Quote:

Originally Posted by Moo
Hello,

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.

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.
• Aug 22nd 2008, 05:37 AM
Moo
Quote:

Originally Posted by magentarita
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.
• Aug 22nd 2008, 07:08 AM
nikhil
Check this out
Quote:

Originally Posted by magentarita
Let t = theta for short

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)

f(t)=csc(t)
f(a)=csc(a)=2
so f(-a)=csc(-a)=-csc(a)=-2 (as csc(a)=2 )
2) f(a) + f(a + 2pi) + f(a + 4pi)
=csc(a)+csc(a+2pi)+csc(a+4pi)
=csc(a)+csc(a)+csc(a)
(csc(t+2n pi) where n is a integer =csc(t))
=2+2+2=6 hence
f(a) + f(a + 2pi) + f(a + 4pi)=6
hope this helps
• Aug 22nd 2008, 12:25 PM
magentarita
Thanks
Quote:

Originally Posted by magentarita
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.

Quote:

Originally Posted by nikhil
f(t)=csc(t)
f(a)=csc(a)=2
so f(-a)=csc(-a)=-csc(a)=-2 (as csc(a)=2 )
2) f(a) + f(a + 2pi) + f(a + 4pi)
=csc(a)+csc(a+2pi)+csc(a+4pi)
=csc(a)+csc(a)+csc(a)
(csc(t+2n pi) where n is a integer =csc(t))
=2+2+2=6 hence
f(a) + f(a + 2pi) + f(a + 4pi)=6
hope this helps