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': 'u06-l01', 'number': 1, 'title': 'Reciprocal, Quotient & Pythagorean Identities', 'family': 'identities', 'week': 16, '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'}
Rewrite tan x using sine and cosine.
2. {'id': 'u06-l01', 'number': 1, 'title': 'Reciprocal, Quotient & Pythagorean Identities', 'family': 'identities', 'week': 16, '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'}
Simplify 1−sin²x.
3. {'id': 'u06-l01', 'number': 1, 'title': 'Reciprocal, Quotient & Pythagorean Identities', 'family': 'identities', 'week': 16, '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'}
Simplify sec²x−tan²x.
4. {'id': 'u06-l01', 'number': 1, 'title': 'Reciprocal, Quotient & Pythagorean Identities', 'family': 'identities', 'week': 16, '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'}
Expand sin(a+b).
5. {'id': 'u06-l01', 'number': 1, 'title': 'Reciprocal, Quotient & Pythagorean Identities', 'family': 'identities', 'week': 16, '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'}
Write cos(2x) in terms of cosine only.
6. {'id': 'u06-l01', 'number': 1, 'title': 'Reciprocal, Quotient & Pythagorean Identities', 'family': 'identities', 'week': 16, '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'}
Evaluate sin75° exactly.
7. {'id': 'u06-l02', 'number': 2, 'title': 'Strategies for Verifying Identities', 'family': 'identities', 'week': 16, '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'}
Rewrite tan x using sine and cosine.
8. {'id': 'u06-l02', 'number': 2, 'title': 'Strategies for Verifying Identities', 'family': 'identities', 'week': 16, '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'}
Simplify 1−sin²x.
9. {'id': 'u06-l02', 'number': 2, 'title': 'Strategies for Verifying Identities', 'family': 'identities', 'week': 16, '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'}
Simplify sec²x−tan²x.
10. {'id': 'u06-l02', 'number': 2, 'title': 'Strategies for Verifying Identities', 'family': 'identities', 'week': 16, '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'}
Expand sin(a+b).
11. {'id': 'u06-l02', 'number': 2, 'title': 'Strategies for Verifying Identities', 'family': 'identities', 'week': 16, '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'}
Write cos(2x) in terms of cosine only.
12. {'id': 'u06-l02', 'number': 2, 'title': 'Strategies for Verifying Identities', 'family': 'identities', 'week': 16, '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'}
Evaluate sin75° exactly.