1. Features of sinusoidal functions
Sal introduces the main features of sinusoidal functions: midline, amplitude, & period. He shows how these can be found from a sinusoidal function's graph.
2. Amplitude & period of sinusoidal functions from equation
Sal finds the amplitude and the period of y=-0.5cos(3x).
3. Amplitude of sinusoidal functions from graph
Given the graph of a sinusoidal function, determine its amplitude.
4. Midline of sinusoidal functions from graph
Given the graph of a sinusoidal function, determine its midline equation.
5. Period of sinusoidal functions from graph
Given the graph of a sinusoidal function, determine its period.
7. Solving cos(θ)=1 and cos(θ)=-1
Sal solves the equations cos(θ)=1 and cos(θ)=-1 using the graph of y=cos(θ).
8. Intersection points of y=sin(x) and y=cos(x)
Sal draws the graphs of the sine and the cosine functions and analyzes their intersection points.
9. Transforming sinusoidal graphs: vertical stretch & horizontal reflection
Sal graphs y=2*sin(-x) by considering it as a vertical stretch and a horizontal reflection of y=sin(x).
10. Transforming sinusoidal graphs: vertical & horizontal stretches
Sal graphs y=-2.5*cos(1/3*x) by considering it as a vertical stretch and reflection, and a horizontal stretch, of y=cos(x).
11. Finding a sinusoidal function from its graph
Sal determines a function of the form y=a*sin(bx) or y=a*cos(bx) based on the graph of the function.
12. Graph sinusoidal functions
Given the formula of a sinusoidal function of the form a*f(bx)+d, draw its graph.
13. Sinusoidal function from graph
Sal finds the equation of a sinusoidal function from its graph where the minimum point (-2,-5) and the maximum point (2,1) are highlighted.