Draw the graph of the following function on the given interval. [4 marks]
y=1.8cos(2x+〖30〗^o ) -〖180〗^o≤x<〖180〗^o
4. Draw the graph of the following function on the given interval. [4 marks]
y=1.8cos(2x+〖30〗^o ) -〖180〗^o≤x<〖180〗^o
To draw the graph of the function y = 1.8cos(2x + 30°) on the interval -180° ≤ x < 180°, follow these steps:
Step 1: Identify key points and features
The key points and features of the function can be determined by analyzing the general form of the cosine function:
y = A cos(Bx + C)
In this case, the key points and features are:
A = amplitude = 1.8
B = frequency = 2
C = phase shift = -30°
Step 2: Determine the period
The period of a cosine function is given by 2π/B. In this case, B = 2, so the period is 2π/2 = π.
Step 3: Plot the x-axis and y-axis
Draw the x-axis and y-axis on a graph, labeling the x-axis with appropriate intervals, such as -180°, -90°, 0°, 90°, and 180°.
Step 4: Plot the amplitude
Since the amplitude is 1.8, mark points on the y-axis at 1.8 and -1.8.
Step 5: Plot the phase shift
The phase shift of -30° means that the graph is shifted to the left by 30°. To determine the starting position, divide the period (π) by the phase shift (-30°) to find the fraction of the period the function has been shifted. In this case, the starting position is 30° * (π/180°) ≈ 0.52.
Step 6: Plot the points
Start from the starting position and plot points at regular intervals of π (the period), such as -π, -π/2, 0, π/2, π.
Calculate the corresponding y-values by substituting the x-values into the function y = 1.8cos(2x + 30°).
For example, when x = 0, y = 1.8cos(2*0 + 30°) ≈ 0.55.
Step 7: Complete the graph
Using the points plotted, draw a smooth curve that represents the cosine function.
Remember to properly label the axes, title the graph, and indicate any key features such as amplitude and phase shift.
By following these steps, you should be able to accurately draw the graph of the function y = 1.8cos(2x + 30°) on the given interval -180° ≤ x < 180°.