University:
Carleton College
Course:
MATH 111 | Introduction to Calculus
Academic year:

2024
Views:

226

Pages:

6
Author:

5CelestialChronicle

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 (0,1), (1,0), (0,1), (1,0) 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 y = sin θ or y = cos θ. Next, write the transformations IN THE ORDER IN WHICH THEY OCCUR. Last, graph each transformation - one at a time. 1. y = -sinθ Amplitude: 1 Reflection: Yes Phase Shift: None Vertical Shift: None Transformations: Reflect over the x-axis graph of y = sinθ 2. y = 2cosθ Amplitude: 2 Reflection: None Phase Shift: None Vertical Shift: None Transformations: Vertical Stretch of 2 graph of y = 2cosθ 3. y = 1/2 cosθ Amplitude: 1/2 Reflection: None Phase Shift: None Vertical Shift: None Transformations: Vertical Shrink of 1/2 4. y = -3sinθ Amplitude: 3 Reflection: Yes Phase Shift: None Vertical Shift: None Transformations: Vertical Stretch of 3 Reflect over the x-axis 5. y = cosθ - 1 Amplitude: 1 Reflection: None Phase Shift: None Vertical Shift: Down 1 Transformations: Down 1 6. y = sinθ + 2 Amplitude: 1 Reflection: None Phase Shift: None Vertical Shift: Up 2 Transformations: Up 2