Keyword: Trigonometry

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Formules

Source: https://www.quora.com/What-are-the-all-trigonometry-formula Angle-Sum and Difference Identities sin (α + β) = sin (α)cos (β) + cos (α)sin (β) sin (α – β) = sin (α)cos (β) – cos (α)sin (β) cos (α + β) = cos (α)cos (β) – sin (α)sin (β) cos (α – β) = cos (α)cos (β) + sin (α)sin (β) tan (A + B) = (tan A + tan B)/(1 - tan A tan B) tan (A - B) = (tan A - tan B)/(1 + tan A tan B) cot (A + B) = (cot A cot B - 1)/(cot A + cot B) cot (A - B) = (cot A cot B + 1)/(cot B - cot A)

Multiple Angle Identities sin 2A = 2 sin A cos A = 2 tan A/ (1 + tan2A) cos 2A = (1 - tan2A)/(1 + tan2A) tan 2A = 2 tan A/(1 - tan2A) sin 3A = 3 sin A – 4 sin3A sin 3A = 4 sin (60° - A) sin A sin (60° + A) cos 3A = 4 cos3A – 3 cos A cos 3A = 4 cos (60° - A) cos A cos (60° + A) tan 3A = tan (60° - A) tan A tan (60° + A) tan 3A = (3tan A – tan3A)/(1 - 3tan2A) (provided A ≠ nπ + π/6)

Half-Angle Identities sin A/2 = ± √(1 - cos A)/ 2 cos A/2 = ± √(1 + cos A)/ 2 tan A/2 = ± √(1 - cos A)/(1 + cos A)

Other Important Formulae sin A + sin B = 2 sin (A+B)/2 . cos (A-B)/2 sin A - sin B = 2 cos (A+B)/2 . sin (A-B)/2 cos A + cos B = 2 cos (A+B)/2 . cos (A-B)/2 cos A - cos B = 2 sin (A+B)/2 . sin (B-A)/2 tan A ± tan B = sin (A ± B)/ cos A cos B, provided A ≠ nπ + π/2, B ≠ mπ cot A ± cot B = sin (B ± A)/ sin A sin B, provided A ≠ nπ, B ≠ mπ+ π/2 1 + tan A tan B = cos (A-B)/ cos A cos B 1 - tan A tan B = cos (A+B)/ cos A cos B

Product Identities 2 sin A cos B = sin (A+B) + sin (A-B) 2 cos A sin B = sin (A+B) - sin (A-B) sin2 A + sin A = 2 2 cos A cos B = cos (A+B) + cos (A-B) 2 sin A sin B = cos (A-B) – cos (A+B)

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Exercice : Trouver la ligne la plus courte entre deux colliders capsule en utilisant les mathématiques.