Trigonometry (Ratios, Identities, Equations): One-Page Formula Sheet

Trigonometry (Ratios, Identities, Equations) — formula sheet

Formulas

• sin(A ± B) = sinA cosB ± cosA sinB
• cos2A = 1 − 2sin²A = 2cos²A − 1
• tan(A + B) = (tanA + tanB)/(1 − tanA tanB)
• cos x = cos α → x = 2nπ ± α

Key ideas

• sin²x + cos²x = 1 is the base identity
• Use ASTC to find signs by quadrant
• General solution of sin x = sin α: x = nπ + (−1)ⁿα
• Sum-to-product formulas simplify sums of sines

Traps to avoid

• Losing solutions when dividing by a trig function
• Wrong general solution form
• Domain restrictions on tan and sec

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