GRAFIK FUNGSI TRIGONOMETRI (1) : y =sin x , y = cos x , y = tan x

Introduction

This tutorial will guide you through understanding the graphs of the basic trigonometric functions: sine (sin), cosine (cos), and tangent (tan). These functions are fundamental in mathematics and are widely used in various fields, including physics, engineering, and computer science. By the end of this tutorial, you will be able to visualize and interpret these functions' graphs.

Step 1: Understanding the Sine Function

• The sine function is represented as y = sin x.
• It oscillates between -1 and 1, creating a wave-like pattern.
• Key points to note:
  • The period of the sine wave is 2π, meaning it repeats every 2π radians.
  • The sine function starts at (0, 0).
  • Important points on the graph are:
    • (0, 0)
    • (π/2, 1)
    • (π, 0)
    • (3π/2, -1)
    • (2π, 0)

Practical Tips

• Use graphing tools or software to visualize the sine function.
• Note the symmetry of the sine wave; it is an odd function, meaning sin(-x) = -sin(x).

Step 2: Exploring the Cosine Function

• The cosine function is represented as y = cos x.
• It also oscillates between -1 and 1 but starts at its maximum value.
• Key points to note:
  • The period of the cosine wave is also 2π.
  • The cosine function starts at (0, 1).
  • Important points on the graph are:
    • (0, 1)
    • (π/2, 0)
    • (π, -1)
    • (3π/2, 0)
    • (2π, 1)

Practical Tips

• Observe that the cosine function is an even function, hence cos(-x) = cos(x).
• Compare the sine and cosine graphs to understand their phase difference of π/2 radians.

Step 3: Analyzing the Tangent Function

• The tangent function is represented as y = tan x.
• Unlike sine and cosine, tangent has a different range and periodicity.
• Key points to note:
  • The period of the tangent function is π.
  • The tangent function has vertical asymptotes where cos x = 0 (e.g., at x = π/2, 3π/2).
  • Important points on the graph are:
    • (0, 0)
    • (π/4, 1)
    • (π/2, undefined)
    • (3π/4, -1)
    • (π, 0)

Practical Tips

• The tangent function is periodic and repeats every π radians.
• Be cautious of the asymptotes where the function is undefined.

Conclusion

In this tutorial, you learned how to graph and interpret the sine, cosine, and tangent functions. Understanding these functions is essential for further studies in trigonometry and calculus. To deepen your knowledge, consider exploring transformations of these functions, such as amplitude changes and phase shifts, and practice plotting them by hand or using graphing software.