Khaemenes Academy · Open-Age Mathematics

Unit 06 Foundation Practice

Guided review with smaller steps and reference formulas.

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.

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