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Trigonometric Ratios

(Move the point labeled "Move" to adjust the dimensions of the triangle.)
(Move the point labeled "Move" to adjust the dimensions of the triangle.)
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Sides of the right triangle: Adjacent = a Opposite = b Hypoteneuse = c Angles of the right triangle: the angle opposite a = A the angle opposite b = B the angle opposite c = C SOHCAHTOA: SOH: Opposite / Hypoteneuse = sin(θ) = b / c CAH: Adjacent / Hypoteneuse = cos(θ) = a / c TOA: Opposite / Adjacent = tan(θ) = b / a Hypoteneuse / Opposite = csc(θ) = c / b = 1 / sin(θ) Hypoteneuse / Adjacent = sec(θ) = c / a = 1 / cos(θ) Adjacent / Opposite = cot(θ) = a / b = 1 / tan(θ) Other Functions: 1 = csc(θ)^2 - cot(θ)^2 1 = sec(θ)^2 - tan(θ)^2 1 = sin(θ)^2 + cos(θ)^2 1 = sec(θ) - exsec(θ) 1 = csc(θ) - coexsec(θ) 1 = vers(θ) + cos(θ) 1 = sin(θ) + covers(θ) hav(θ) = vers(θ) / 2 Pythagorean Theorem: c^2 = a^2 + b^2 Law of Sines: 2 * r = a / sin(A) = b / sin(B) = c / sin(C) where "r" is the radius of the circumcircle Law of Cosines: cos(A) = (c^2 + b^2 - a^2) / (2 * b * c) Law of Tangents: (a + b) / (a - b) = tan((A + B) / 2) / tan((A - B) / 2) Dot Product: A · B = cos(θ) = xA * xB + yA * yB where A and B are vectors with lengths equal to 1