Draw the graph of Y=Sinx for 0 degrees less than or equal to x less than or equal to 360 degrees
State the axis of symmetry
period
amplitude
any book on trig will show this graph, and explain all the above topics.
Where do you get stuck?
No answer
To draw the graph of y = sin(x) for 0 degrees ≤ x ≤ 360 degrees:
1. Plot the x and y-axis on a coordinate plane.
2. The graph of y = sin(x) starts at the origin (0, 0).
3. Start at 0 degrees (0 radians) on the x-axis and go in a counter-clockwise direction.
4. At 0 degrees, the value of sin(0) is 0, so the point is (0, 0).
5. As you move to 90 degrees, the value of sin(90) is 1, so the point is (90, 1).
6. At 180 degrees, the value of sin(180) is 0, so the point is (180, 0).
7. At 270 degrees, the value of sin(270) is -1, so the point is (270, -1).
8. Finally, at 360 degrees, the value of sin(360) is 0, so the point is (360, 0).
The points (0, 0), (90, 1), (180, 0), (270, -1), and (360, 0) will form a wave-like shape known as a sine wave.
Axis of Symmetry:
The axis of symmetry for the graph of y = sin(x) is the y-axis (x = 0). This means that the graph is symmetric with respect to the y-axis.
Period:
The period of the graph is 360 degrees (or 2π radians). This means that the pattern repeats itself every 360 degrees (or 2π radians).
Amplitude:
The amplitude of the graph is 1. This means that the graph oscillates between y-values of -1 and 1, with a maximum value of 1 and a minimum value of -1.
To draw the graph of y = sin(x) for 0 degrees ≤ x ≤ 360 degrees, follow these steps:
1. First, understand the basic shape of the sine function. The graph of y = sin(x) is a wave that oscillates between -1 and 1.
2. Plot the points for key angles. Start by determining the angles at which the sine function passes through its extreme points (-1 and 1). These angles are 0°, 90°, 180°, 270°, and 360°. For example, at 0°, sin(0°) = 0, so plot the point (0°, 0). Similarly, at 90°, sin(90°) = 1, so plot the point (90°, 1).
3. Connect the points. Use a smooth curve to connect the plotted points, creating a wave-like shape that repeats.
4. Determine the axis of symmetry. In the case of y = sin(x), the axis of symmetry is the y-axis (x = 0). This means that the graph is symmetrical with respect to the y-axis.
5. Identify the period. The period of the sine function is the distance it takes for one complete cycle. In this case, the period is 360° because the graph repeats itself every 360°. So, one complete cycle goes from 0° to 360°.
6. Find the amplitude. The amplitude of the sine function is the distance from the midline (y = 0) to the highest or lowest point of the graph. In this case, the amplitude is 1 because the sine function oscillates between -1 and 1. Therefore, the highest point on the graph is (90°, 1), and the lowest point is (270°, -1).
By following these steps, you should be able to draw the graph of y = sin(x) for 0 degrees ≤ x ≤ 360 degrees and identify its axis of symmetry, period, and amplitude.