Trigonometric Ratios

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

Information: Trigonometric Ratios