Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u06-l07', 'number': 7, 'title': 'Solving Multi-Step Equations on Intervals', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve sin x=1/2 on [0,2π).
2. {'id': 'u06-l07', 'number': 7, 'title': 'Solving Multi-Step Equations on Intervals', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve cos x=−√2/2 on [0,2π).
3. {'id': 'u06-l07', 'number': 7, 'title': 'Solving Multi-Step Equations on Intervals', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve tan x=1 on [0,2π).
4. {'id': 'u06-l07', 'number': 7, 'title': 'Solving Multi-Step Equations on Intervals', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve 2sin x−1=0 on [0,2π).
5. {'id': 'u06-l07', 'number': 7, 'title': 'Solving Multi-Step Equations on Intervals', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Give the general solution of cos x=1.
6. {'id': 'u06-l07', 'number': 7, 'title': 'Solving Multi-Step Equations on Intervals', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Why must solutions be checked after squaring an equation?
7. {'id': 'u06-l08', 'number': 8, 'title': 'General Solutions, Technology & Extraneous Results', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve sin x=1/2 on [0,2π).
8. {'id': 'u06-l08', 'number': 8, 'title': 'General Solutions, Technology & Extraneous Results', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve cos x=−√2/2 on [0,2π).
9. {'id': 'u06-l08', 'number': 8, 'title': 'General Solutions, Technology & Extraneous Results', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve tan x=1 on [0,2π).
10. {'id': 'u06-l08', 'number': 8, 'title': 'General Solutions, Technology & Extraneous Results', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Solve 2sin x−1=0 on [0,2π).
11. {'id': 'u06-l08', 'number': 8, 'title': 'General Solutions, Technology & Extraneous Results', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Give the general solution of cos x=1.
12. {'id': 'u06-l08', 'number': 8, 'title': 'General Solutions, Technology & Extraneous Results', 'family': 'trigeq', 'week': 18, 'unit': 6, 'unit_title': 'Trigonometric Identities & Equations', 'essential': 'How can equivalent forms, identities, algebraic reasoning, and interval analysis simplify expressions and solve trigonometric equations?', 'project': 'Identity Proof Portfolio & Equation Audit'}
Why must solutions be checked after squaring an equation?