Trigonometry Laws And Identities

Law of Sines

sin(A)/a = sin(B)/b = sin(C)/c

Law of Cosines

a² = b² + c² - 2bccos(A)

Trigonometric Identities

sin = opp/hyp, cos = adj/hyp, tan = opp/adj, cot = adj/opp, csc = hyp/opp, sec = hyp/adj

Unit Circle

Circle with radius 1 centered at the origin:Sine along the y-axis, cosine along the x-axis

Pythagorean’s Theorem

a² + b² = c²

Pythagorean’s Identities

sin²a + cos²a = 1, tan²a + 1 = sec²a, cot²a + 1 = csc²a

Even/Odd Identities

sin(-a) = -sin(a), cos(-a) = cos(a), tan(-a) = -tan(a), cot(-a) = -cot(a), csc(-a) = -csc(a), sec(-a) = sec(a)

Double Angle Identities

sin(2a) = 2sin(a)cos(a), cos(2a) = cos²(a) - sin²(a) = 2cos²(a) - 1 = 1 - 2sin²(a), tan(2a) = 2tan(a) / (1 - tan²(a))

Half Angle Identities

cos(a/2) = ±√(1 + cos(a)/2), sin(a/2) = ±√(1 - cos(a)/2), tan(a/2) = ±√((1 - cos(a)) / (1 + cos(a)))