Full unit practice requiring complete reasoning and representation checks.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u05-l01', 'number': 1, 'title': 'Graphing Sine and Cosine from the Unit Circle', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
For y=4sin(3x)−2, state the amplitude.
2. {'id': 'u05-l01', 'number': 1, 'title': 'Graphing Sine and Cosine from the Unit Circle', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
For y=4sin(3x)−2, state the period.
3. {'id': 'u05-l01', 'number': 1, 'title': 'Graphing Sine and Cosine from the Unit Circle', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
For y=2cos(x−π/4)+1, state the phase shift.
4. {'id': 'u05-l01', 'number': 1, 'title': 'Graphing Sine and Cosine from the Unit Circle', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
State the midline of y=−3sin(2x)+5.
5. {'id': 'u05-l01', 'number': 1, 'title': 'Graphing Sine and Cosine from the Unit Circle', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
State one vertical asymptote of y=tan x.
6. {'id': 'u05-l01', 'number': 1, 'title': 'Graphing Sine and Cosine from the Unit Circle', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
A periodic quantity ranges from 8 to 20. Find amplitude and midline.
7. {'id': 'u05-l02', 'number': 2, 'title': 'Amplitude, Period, Midline & Phase Shift', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
For y=4sin(3x)−2, state the amplitude.
8. {'id': 'u05-l02', 'number': 2, 'title': 'Amplitude, Period, Midline & Phase Shift', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
For y=4sin(3x)−2, state the period.
9. {'id': 'u05-l02', 'number': 2, 'title': 'Amplitude, Period, Midline & Phase Shift', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
For y=2cos(x−π/4)+1, state the phase shift.
10. {'id': 'u05-l02', 'number': 2, 'title': 'Amplitude, Period, Midline & Phase Shift', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
State the midline of y=−3sin(2x)+5.
11. {'id': 'u05-l02', 'number': 2, 'title': 'Amplitude, Period, Midline & Phase Shift', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
State one vertical asymptote of y=tan x.
12. {'id': 'u05-l02', 'number': 2, 'title': 'Amplitude, Period, Midline & Phase Shift', 'family': 'triggraph', 'week': 13, 'unit': 5, 'unit_title': 'Trigonometric Functions, Graphs & Periodic Models', 'essential': 'How do amplitude, period, phase, midline, and reciprocal behavior describe and model repeating phenomena?', 'project': 'Periodic Phenomenon Model & Residual Analysis'}
A periodic quantity ranges from 8 to 20. Find amplitude and midline.