Graph of the sine function | Summary and Q&A

TL;DR

Learn how to define and graph the sine function, which represents oscillatory motion between 1 and -1.

Key Insights

• ⭕ Trigonometric functions can be defined using a unit circle and the coordinates where the radius intersects the circle.
• 🧡 Sine represents oscillatory motion and ranges from -1 to 1, forming a wave-like pattern.
• 👨‍💼 The graph of the sine function resembles a sine wave and can be extended infinitely in both directions.
• 🤨 The values of the sine function at specific angles (0, pi/2, pi, 3pi/2, 2pi) help in graphing the function accurately.
• 👨‍💼 The sine function is cyclic and repeats every 2pi radians.
• 🟡 The y-coordinate of the point where the radius intersects the unit circle represents the sine value.
• 😀 The graph of the sine function is symmetrical about the y-axis.

Transcript

Hello. In the last presentation we kind of re-defined the sine, the cosine, and the tangent functions in a broader way where we said if we have a unit circle and our theta is, or our angle, is -- let me use the right tool -- let's say, and our angle is the angle between, say, the x-axis and a radius in the unit circle, and this is our radius. the c... Read More

Questions & Answers

Q: How are sine, cosine, and tangent defined using a unit circle?

Sine is represented by the y-coordinate, cosine by the x-coordinate, and tangent by the ratio of y over x at the point where the radius intersects the unit circle.

Q: What are the values of the sine function at specific angles?

When theta is 0 radians, sine is 0. At pi/2, sine is 1. At pi, sine is 0. At 3pi/2, sine is -1. At 2pi, sine is 0.

Q: How is the graph of the sine function constructed?

The graph starts at (0,0) and goes through the points (pi/2, 1), (pi,0), and (3pi/2, -1), before returning to (2pi, 0). It forms a wave-like pattern oscillating between 1 and -1.

Q: Can the sine function be extended beyond the given angles?

Yes, the graph of the sine function can be extended indefinitely in both directions, oscillating between 1 and -1 and producing a continuous sine wave.

Summary & Key Takeaways

• Trigonometric functions can be defined using a unit circle, with the sine function representing the y-coordinate of where the radius intersects the circle.

• By evaluating specific angles (0, pi/2, pi, 3pi/2, 2pi), the sine function can be graphed as a wave oscillating between 1 and -1.

• The graph of the sine function resembles a sine wave and can be extended indefinitely in both directions.