Mrs. Jimenez
Honors Algebra 2/Trig. B
Golden Valley High School
Name _____________________ Period ___
Signature ______________ Date ________
Graphing Sine and Cosine Functions (6.4)
Directions: Graph each function for one period on the first graph. In each case, specify the amplitude, the
period, the phase shift, any x-intercept(s), the y-intercept, and the maximum and minimum points for the first
period of the function. Then, on the second graph sketch the trigonometric function from zero to 2π.
1. y = 3sin x
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
2. y = −2.5cos x
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
3. y = −4 sin2x
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
3
x
4. y = cos
2
4
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
⎛
π⎞
5. y = 2cos⎜ x − ⎟
⎝
2⎠
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
6. y = −2sin( πx + π )
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
⎛
π⎞
7. y = 3sin⎜2x − ⎟ −1
⎝
2⎠
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1
⎛π
⎞
8. y = − cos ⎜ x + π ⎟ + 3
⎝2
⎠
Amplitude: ______
Period: _______
Phase Shift: _______
Maximums: ________________________
y-intercept: ______
x-intercept(s): ______________________
Minimums: ________________________
1