Trigonometri Matematika Kelas 10 • Part 32: Menggambar Grafik Fungsi y=cos x dengan Lingkaran Satuan

Summary

In this educational video, the presenter explains how to graph the trigonometric function y = cos(x) using the unit circle, with a detailed walkthrough of the values at special angles from 0° to 360°. The video covers two methods for graphing: one using a table of cos(x) values and the other by referencing the unit circle. The video also explores key concepts such as amplitude, period, and maximum/minimum values, as well as the function's domain and range, providing a comprehensive guide to understanding and graphing cosine functions.

Takeaways

• 😀 The video explains how to graph the trigonometric function y = cos(x) for 0° ≤ x ≤ 360° using the unit circle.
• 😀 A table of cosine values for special angles (0°, 30°, 45°, 60°, etc.) is created to help plot the graph accurately.
• 😀 The cosine values for specific angles are discussed, such as cos(0°) = 1, cos(90°) = 0, and cos(180°) = -1.
• 😀 The graph of y = cos(x) is different from y = sin(x) in terms of how the angles are measured and where the graph starts.
• 😀 The unit circle is used to visualize the function, where the cosine of an angle corresponds to the vertical height from the center of the unit circle.
• 😀 Cosine values are plotted on a coordinate plane with angles along the x-axis and cosine values along the y-axis.
• 😀 The graph oscillates between 1 (maximum value) and -1 (minimum value), with a period of 360° and amplitude of 1.
• 😀 The maximum value of the graph occurs at x = 0° and x = 360°, while the minimum value occurs at x = 180°.
• 😀 The amplitude of the cosine function is 1, which is the distance from the centerline (x-axis) to the highest or lowest point on the graph.
• 😀 The domain of the function is 0° ≤ x ≤ 360°, and the range is -1 ≤ y ≤ 1, reflecting the behavior of the cosine function over one full period.

Q & A

What is the main topic of this video?

The main topic of the video is how to draw the graph of the trigonometric function y = cos(X) using the unit circle.

What is the range of X for the graph of y = cos(X) in this video?

The range of X for the graph of y = cos(X) is from 0° to 360°.

What are the two methods mentioned for drawing the graph of y = cos(X)?

The two methods mentioned are using a table with special angles and using the unit circle.

How is the table used to find the values of cos(X)?

The table lists special angles from 0° to 360° and provides the corresponding values of cos(X) for each angle, such as cos(0°) = 1, cos(30°) = √3/2, and so on.

What is the significance of the unit circle in drawing the graph of y = cos(X)?

In the unit circle method, the graph is drawn by measuring the angle from the center of the circle and using the vertical line from the center to find the value of cos(X) at each angle.

How do you determine the value of cos(X) at 30° using the unit circle method?

At 30°, you measure the angle from the center of the unit circle, then draw a vertical line to the right to find the corresponding value of cos(30°), which is √3/2.

What is the maximum and minimum value of cos(X) from the graph?

The maximum value of cos(X) is 1, which occurs at 0° and 360°, and the minimum value is -1, which occurs at 180°.

What does the amplitude of the function y = cos(X) represent?

The amplitude of the function y = cos(X) is the distance from the midline (y = 0) to the maximum or minimum value, which is 1 in this case.

What is the period of the function y = cos(X)?

The period of the function y = cos(X) is 360°, meaning the pattern repeats every 360°.

What is the domain and range of the function y = cos(X)?

The domain of y = cos(X) is 0° ≤ X ≤ 360°, and the range is -1 ≤ y ≤ 1, as cos(X) takes values between -1 and 1.