The Graph of Sin(x)

The following table shows the value of [Graphics:Images/index_gr_1.gif] for various values of x.  (Namely all multiples of 30° and 45°, except we're using radians.)  You don't have to memorize these values; you can find all of them using our unit-circle definitions and by fitting a 45°-45°-90° or 30°-60°-90° triangle into the circle.  We did this during the lecture on section 5.2.

x 0 [Graphics:Images/index_gr_2.gif] [Graphics:Images/index_gr_3.gif] [Graphics:Images/index_gr_4.gif] [Graphics:Images/index_gr_5.gif] [Graphics:Images/index_gr_6.gif] [Graphics:Images/index_gr_7.gif] [Graphics:Images/index_gr_8.gif] π [Graphics:Images/index_gr_9.gif] [Graphics:Images/index_gr_10.gif] [Graphics:Images/index_gr_11.gif] [Graphics:Images/index_gr_12.gif] [Graphics:Images/index_gr_13.gif] [Graphics:Images/index_gr_14.gif] [Graphics:Images/index_gr_15.gif] [Graphics:Images/index_gr_16.gif]
y=sin(x) 0 [Graphics:Images/index_gr_17.gif] [Graphics:Images/index_gr_18.gif] [Graphics:Images/index_gr_19.gif] 1 [Graphics:Images/index_gr_20.gif] [Graphics:Images/index_gr_21.gif] [Graphics:Images/index_gr_22.gif] 0 [Graphics:Images/index_gr_23.gif] [Graphics:Images/index_gr_24.gif] [Graphics:Images/index_gr_25.gif] [Graphics:Images/index_gr_26.gif] [Graphics:Images/index_gr_27.gif] [Graphics:Images/index_gr_28.gif] [Graphics:Images/index_gr_29.gif] 0

If we plot these points [Graphics:Images/index_gr_30.gif]  they look like this:

[Graphics:Images/index_gr_31.gif]

If we connect the dots using a smooth curve, we'll get the following graph.

[Graphics:Images/index_gr_32.gif]

[Graphics:Images/index_gr_33.gif]

We know that [Graphics:Images/index_gr_34.gif] is periodic with period 2π.  That means the graph just repeats forever and ever to the left and right.

[Graphics:Images/index_gr_35.gif]

The Graph of Cos(x)

[Note that this section is almost identical to the previous section; all I've done is replaced references to [Graphics:Images/index_gr_36.gif] with references to [Graphics:Images/index_gr_37.gif].]

The following table shows the value of [Graphics:Images/index_gr_38.gif] for various values of x.  (Namely all multiples of 30° and 45°, except we're using radians.)  You don't have to memorize these values; you can find all of them using our unit-circle definitions and by fitting a 45°-45°-90° or 30°-60°-90° triangle into the circle.  We did this during the lecture on section 5.2.

x 0 [Graphics:Images/index_gr_39.gif] [Graphics:Images/index_gr_40.gif] [Graphics:Images/index_gr_41.gif] [Graphics:Images/index_gr_42.gif] [Graphics:Images/index_gr_43.gif] [Graphics:Images/index_gr_44.gif] [Graphics:Images/index_gr_45.gif] π [Graphics:Images/index_gr_46.gif] [Graphics:Images/index_gr_47.gif] [Graphics:Images/index_gr_48.gif] [Graphics:Images/index_gr_49.gif] [Graphics:Images/index_gr_50.gif] [Graphics:Images/index_gr_51.gif] [Graphics:Images/index_gr_52.gif] [Graphics:Images/index_gr_53.gif]
y=cos(x) 1 [Graphics:Images/index_gr_54.gif] [Graphics:Images/index_gr_55.gif] [Graphics:Images/index_gr_56.gif] 0 [Graphics:Images/index_gr_57.gif] [Graphics:Images/index_gr_58.gif] [Graphics:Images/index_gr_59.gif] [Graphics:Images/index_gr_60.gif] [Graphics:Images/index_gr_61.gif] [Graphics:Images/index_gr_62.gif] [Graphics:Images/index_gr_63.gif] 0 [Graphics:Images/index_gr_64.gif] [Graphics:Images/index_gr_65.gif] [Graphics:Images/index_gr_66.gif] 1

If we plot these points [Graphics:Images/index_gr_67.gif]  they look like this:

[Graphics:Images/index_gr_68.gif]

If we connect the dots using a smooth curve, we'll get the following graph.

[Graphics:Images/index_gr_69.gif]

We know that [Graphics:Images/index_gr_70.gif] is periodic with period 2π.  That means the graph just repeats forever and ever to the left and right.

[Graphics:Images/index_gr_71.gif]


Converted by Mathematica      September 11, 2002