10.3: 2, 3, 8
    10.5: 11
    12.3: 1, 2, 7, 8, 9, 10, 11

[Graphics:Images/calculus_gr_1.gif]

12.3:
    1)  Use:

[Graphics:Images/calculus_gr_2.gif]

    to show that the circular function [Graphics:Images/calculus_gr_3.gif] with period [Graphics:Images/calculus_gr_4.gif] and phase difference [Graphics:Images/calculus_gr_5.gif] can be written as a combination of pure sine and cosine functions of the same period:

[Graphics:Images/calculus_gr_6.gif]

    Show that [Graphics:Images/calculus_gr_7.gif] and [Graphics:Images/calculus_gr_8.gif].

    To start with, lets use the sum trig identity to rewrite our function:

[Graphics:Images/calculus_gr_9.gif]

    Now if we let [Graphics:Images/calculus_gr_10.gif] and [Graphics:Images/calculus_gr_11.gif] we have:

[Graphics:Images/calculus_gr_12.gif]

[Graphics:Images/calculus_gr_13.gif]

[Graphics:Images/calculus_gr_14.gif]

[Graphics:Images/calculus_gr_15.gif]

[Graphics:Images/calculus_gr_16.gif]

[Graphics:Images/calculus_gr_17.gif]

[Graphics:Images/calculus_gr_18.gif]

[Graphics:Images/calculus_gr_19.gif]

    10.5: 11

[Graphics:Images/calculus_gr_20.gif]

[Graphics:Images/calculus_gr_21.gif]

    12.3: 1, 2, 7, 8, 9, 10, 11

[Graphics:Images/calculus_gr_22.gif]

[Graphics:Images/calculus_gr_23.gif]

[Graphics:Images/calculus_gr_24.gif]

[Graphics:Images/calculus_gr_25.gif]

[Graphics:Images/calculus_gr_26.gif]

[Graphics:Images/calculus_gr_27.gif]


Converted by Mathematica      May 24, 2004