Find the Value of the Number C

• Aug 29th 2008, 03:45 AM
magentarita
Find the Value of the Number C
Find the value of the number C:

(1/2)[cos^2(x)] + C = (1/4)[cos2(x)]
• Aug 29th 2008, 04:16 AM
mr fantastic
Quote:

Originally Posted by magentarita
Find the value of the number C:

(1/2)[cos^2(x)] + C = (1/4)[cos2(x)]

Since it's an identity, it's true for all values of x. So substitute a simple value like x = 0. Then solve for C .....
• Aug 29th 2008, 04:16 AM
nikhil
Quote:

Originally Posted by magentarita
Find the value of the number C:

(1/2)[cos^2(x)] + C = (1/4)[cos2(x)]

Cos2x=2(cosx)^2-1 therfor
(cosx)^2=(1+cos2x)/2
as
(1/2)[cos^2(x)] +C=(1/4)[cos2(x)]
1/2((1+cos2x)/2)+C=(1/4)[cos2(x)]
1/4+(cos2x)/4+C=(1/4)[cos2(x)]
1/4+C=0
C=-1/4
• Aug 29th 2008, 04:40 AM
mr fantastic
Quote:

Originally Posted by nikhil
Cos2x=2(cosx)^2-1 therfor
(cosx)^2=(1+cos2x)/2
as
(1/2)[cos^2(x)] +C=(1/4)[cos2(x)]
1/2((1+cos2x)/2)+C=(1/4)[cos2(x)]
1/2+(cos2x)/4+C=(1/4)[cos2(x)] Mr F says: That red 2 should be a 4.
1/2+C=0
C=-1/2

Actually C = -1/4.

You should have tested it using a simple value of x lol!!
• Aug 29th 2008, 04:47 AM
nikhil
Ooooopppss