GRAFIK FUNGSI TRIGONOMETRI (COSINUS)

Introduction

This tutorial is designed to help students, especially those in grade X, understand how to graph the cosine function using two effective methods: the unit circle and the table method. By following these steps, you will be able to create accurate graphs of trigonometric functions and enhance your understanding of their properties.

Step 1: Understanding the Cosine Function

• The cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle.
• The general form of the cosine function is written as:
  • y = cos(x)
• Key characteristics to remember:
  • The cosine function has a range of -1 to 1.
  • It is periodic with a period of 2π.

Step 2: Using the Unit Circle to Graph Cosine

1. Draw the Unit Circle:

   • Start by drawing a circle with a radius of 1, centered at the origin (0,0) on a coordinate plane.

2. Identify Key Angles:

   • Mark the key angles in radians: 0, π/2, π, 3π/2, and 2π.
   • Calculate the cosine values for these angles:
     • cos(0) = 1
     • cos(π/2) = 0
     • cos(π) = -1
     • cos(3π/2) = 0
     • cos(2π) = 1

3. Plot Points:

   • Plot the points on the Cartesian plane:
     • (0, 1)
     • (π/2, 0)
     • (π, -1)
     • (3π/2, 0)
     • (2π, 1)

4. Connect the Points:

   • Draw a smooth curve connecting the plotted points to form one complete cycle of the cosine wave.

Step 3: Using a Table to Summarize Values

1. Create a Table:

   • Set up a table with two columns: Angle (in radians) and Cosine Value.

2. Fill in the Table:

   • Input the key angles and their corresponding cosine values:

     | Angle (radians) | Cosine Value |
     |------------------|--------------|
     | 0                | 1            |
     | π/6              | √3/2         |
     | π/4              | √2/2         |
     | π/3              | 1/2          |
     | π/2              | 0            |
     | π                | -1           |
     | 3π/2             | 0            |
     | 2π               | 1            |
     

3. Plot the Points from the Table:

   • Using the values from the table, plot the points on the graph as before.

4. Draw the Cosine Curve:

   • Connect the points smoothly to illustrate the wave-like nature of the cosine function.

Conclusion

By utilizing both the unit circle and the table method, you can effectively graph the cosine function. Understanding these methods will not only help you in graphing but also deepen your comprehension of trigonometric functions' behavior. For further practice, try graphing other trigonometric functions such as sine and tangent using the same techniques.