This is a free lesson from our course in Trigonometry
In this lesson you'll learn with the help of several examples, practice questions
with solution, video and explanation by instructor how to sketch the graphs of sine and cosine functions and translations of
these functions. To sketch the graph of sine and cosine function, you'll plot the graph in the interval
-<= x <=
. On the graph, you'll
plot the points whose coordinates can be taken from the table having values of
sine and cosine functions for angle measure in radians as well as corresponding angle measure in degrees.(More text below video...)
(Continued from above) Each time you increase or decrease the value of the x-coordinates
by a multiple of 2, the
basic sine or cosine curve is repeated.
Let's take an example of the graph y = sin x. As the angle measure
() increases, the y
coordinate of the point of intersection also increases. When
=
/2, the y coordinate
of the point of intersection attains its highest values i.e. sin
/2 = 1. As the angle
measure continues to increase and lies in quadrant II, the y-coordinate
of the point of intersection begins to decrease. As the angle becomes,
=
, the y coordinate
of the point of intersection decreases and is 0 (sin
= 0). Using the symmetry of the sine function you can graph it over the interval
[-,
], then using the periodic
nature of the sine function, you can graph y = sin x
by repeating this graph. Remember that the sine function is periodic, and its period
is 2. Note that this
might seem complicated here in text, but once you have instructor explain it to
you in their voice and handwriting in the video, you'll find it much simpler.
Likewise the graph of y = cos x follows the similar pattern i.e.
decreasing, increasing and repeating but here, when value of x is 0, value
of y is 1. You'll also explore how to sketch the graphs of y =
sin 2x, y = sin x/2, y = cos 2x and
y = cos x/2.
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<= x <=
) increases, the y
coordinate of the point of intersection also increases. When