Download to read offline
Trigonometric Functions Lecture (brief presentation)
- 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 SineGraph • • 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 TrigFunctions • • Sound waves (sine) • • Ocean tides (sine/cosine) • • Ferris wheel seat height (cosine) • • Electricity (sine wave)
- 8. Interactive Activity: HumanSine 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 • • Trigfunctions are periodic and repeat • • Derived from unit circle • • Sine starts at 0, Cosine starts at 1 • • Tangent = sin/cos with asymptotes