Trigonometry: Graphs of Sine and Cosine Functions
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...)
<h2>Trigonometry - Graphs of Sine and Cosine Functions</h2> <p>graph, sine, cosine, curve, degreesł video, angle, trigonometry, graphs, measure, example, radians, cosine sine function, sine function, cosine function, table, value, graphs of sine and cosine functions, increases, decreases, practice questions, quizzes</p> <p>To sketch the graph of sine and cosine function, we will plot the graph in the interval -pi<= x <= pi. On the graph, we 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.</p>
Other useful lessons:
Definitions of Trigonometric Functions
The unit circle, Sine, and Cosine
(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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