sin

Express the following in the simplest form you can

     a. sin(2pf t - p ) + sin(2pf t + p )

     b. sin(2pf t) + sin(2pf t - p )

sin a + sin b   = 2 sin a + b   .  cos a - b
                                2              2

1. sin (2pft –p) + sin (2pft + p) =

= 2 sin (2pf t - p + 2pf t + p)/2 . cos (2pf t - p -   2pf t - p)/2

= 2 sin 2 pf t . cos -p

= 2 sin 2 pf t . (-1)

= - 2 sin 2 pf t

2. sin (2pft) + sin (2pft – p)

= 2 sin (2pft + 2pft – p)/2 . cos (2pft - 2pft + p)/2

= 2 sin (4 pft – p)/2 . cos 90

= 2 sin 2 pft – 90 . 0

= 0

3.7. Find the period of the function  f (t) = (10 cos t)²

 

f(t) = (10 cos t) ²

     = 100 cos t cos t -> cos²a = ½(1 + cos 2a)     

     = 50 ( 1 + cos2t)

     = 50 ( 1 + cos2p1/pt)

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

Jadi ,  period T = p .