University:
Cornell University
Course:
MATH 1101 | Calculus Preparation
Academic year:

2020
Views:

343

Pages:

6
Author:

StellarSymphony

Advanced Math Review: Graphs of Sine and Cosine Graph a unit circle (in degrees) and label all the points. Using the axis below, graph one cycle of the sine function in one color. Graph one cycle of the cosine function in another color. unit circle with points labeled and graphs of sine and cosine functions *The general form for a sine equation is: y = a sin(b(θ - h)) + k The general form for a cosine equation is: y = a cos(b(θ - h)) + k For each function, state the amplitude, if there is a reflection, the phase shift and the vertical shift. Write "none" for transformations that do not exist. Then, graph the function. Start by graphing the parent function sin θ or cos θ. Next, write the transformations IN THE ORDER IN WHICH THEY OCCUR. Last, graph each transformation - one at a time.* y = -sin θ Amplitude: 1 Reflection: Yes Phase Shift: None Vertical Shift: None Transformations: Reflect over the x-axis graph of y = sin θ y = 2cos θ Amplitude: 2 Reflection: None Phase Shift: None Vertical Shift: None Transformations: Vertical Stretch of 2 graph of y = 2cos θ 3. y = -1/2 cos θ Amplitude: 1/2 Reflection: Yes Phase Shift: None Vertical Shift: None Transformations: Vertical Shrink of 1/2 Reflect over the x-axis [Image of the graph of y = -1/2 cos θ] 4. y = -3 sin θ Amplitude: 3 Reflection: Yes Phase Shift: None Vertical Shift: None Transformations: Vertical Stretch of 3 Reflect over the x-axis [Image of the graph of y = -3 sin θ] 5. y = cos θ - 1 Amplitude: 1 Reflection: None Phase Shift: None Vertical Shift: Down 1 Transformations: Down 1 [Image of the graph of y = cos θ - 1] 6. y = sin θ + 2 Amplitude: 1 Reflection: None Phase Shift: None Vertical Shift: Up 2 Transformations: Up 2 [Image of the graph of y = sin θ + 2]