Trigonometric Functions Lecture (brief presentation)

This presentation contains slides about trigonometric functions, designed for those who have little to no knowledge about these functions.

1. Trigonometric Functions Sine • Cosine • Tangent Visual and Interactive Teaching

2. Real-Life Hook • Ferris wheel motion • Pendulum swing • Ocean tides Ask: What patterns do you notice?

3. Unit Circle • Circle with radius 1 • Point moves counterclockwise • x = cos θ, y = sin θ • Shadows on axes → trig values

4. Building the Sine Graph • Key points: sin(0°)=0, sin(90°)=1, sin(180°)=0, sin(270°)=-1, sin(360°)=0 • Plot points step by step • Connect smoothly → wave

5. Cosine Graph • Key points: cos(0°)=1, cos(90°)=0, cos(180°)=-1, cos(270°)=0, cos(360°)=1 • Similar to sine but shifted left

6. Tangent Function • tan θ = sin θ / cos θ • Undefined when cos θ = 0 (90°, 270°) • Graph has vertical asymptotes

7. Applications of Trig Functions • Sound waves (sine) • Ocean tides (sine/cosine) • Ferris wheel seat height (cosine) • Electricity (sine wave)

8. Interactive Activity: Human Sine Wave • Students stand as 'points' of the sine graph • Assign θ values (0°, 30°, 60°, ...) • Each student shows y = sin θ with height • Together they form a living sine wave!

9. Summary • Trig functions are periodic and repeat • Derived from unit circle • Sine starts at 0, Cosine starts at 1 • Tangent = sin/cos with asymptotes