10.3: 2, 3, 8
10.5: 11
12.3: 1, 2, 7, 8, 9, 10, 11
![[Graphics:Images/calculus_gr_1.gif]](Images/calculus_gr_1.gif)
12.3:
1) Use:
![[Graphics:Images/calculus_gr_2.gif]](Images/calculus_gr_2.gif)
to show that the circular function with period
and phase difference
can be written as a combination of pure sine and cosine functions of the same period:
![[Graphics:Images/calculus_gr_6.gif]](Images/calculus_gr_6.gif)
Show that and
.
To start with, lets use the sum trig identity to rewrite our function:
![[Graphics:Images/calculus_gr_9.gif]](Images/calculus_gr_9.gif)
Now if we let and
we have:
![[Graphics:Images/calculus_gr_12.gif]](Images/calculus_gr_12.gif)
![[Graphics:Images/calculus_gr_19.gif]](Images/calculus_gr_19.gif)
10.5: 11
![[Graphics:Images/calculus_gr_21.gif]](Images/calculus_gr_21.gif)
12.3: 1, 2, 7, 8, 9, 10, 11