Cheatography

Trigonometry Cheat Sheet (DRAFT) by sapphicpenguin

This is a draft cheat sheet. It is a work in progress and is not finished yet. Discri­minant

 b²-4ac > 0 2 real roots b²-4ac = 0 1 repeated root b²-4ac < 0 2 imaginary roots

Supple­mentary & Comple­mentary Angles

 supple­mentary angles add up to 180° comple­mentary angles add up to 90°

Pythag­orean Theorem

 a²+b²=c²

45-45-90 triangles

 a=b c=a√2 or b√2 c/√2=a or b

30-60-90 triangles

 c=2b a=b√3
when a triangle's 3 angles are 30°, 60°, and 90°
a = long leg
b = short leg
c = hypotenuse

Area of a triangle

 AΔ = (1/2)bh

csc, sec, cot - the opposite of SOH-CA­H-TOA

 cosecant hypote­nus­e/o­pposite secant hypote­nus­e/a­djacent cotangent adjace­nt/­opp­osite

Circle Measur­ements

 area πr² diameter 2r circum­ference 2πr OR πd arc length θr
d = diameter
θ = angle

Unit Circle Unit Circle values

 sin y cos x tan y/x csc 1/y sec 1/x cot x/y
for tan & cot, only use the tops of the fractions

Coterminal Angles

 θ ± 360° θ ± 2π

y = a (sin) b (x - c) + d

 a amplitude change b period change c horizontal change: + = left, - = right d vertical change: + = up, - + down -sin(x) reflection across x-axis sin(-x) reflection across y=axis

Amplitude & Period

 amplitude vertical period horizontal
both always positive
tan, cos, sec, cot: no amplitude

Inverses

 sin⁻¹(y) = x sin(x) = y
csc(x) = 1/sin(x)

restri­cting range: usually I & IV
except in cos⁻¹: I & II

Reciprocal Identities

 sinθ = 1/cscθ cscθ = 1/sinθ cosθ = 1/secθ secθ = 1/cosθ tanθ = 1/cotθ cotθ = 1/tanθ

Ratio Identities

 tanθ = sinθ/cosθ cotθ = cosθ/sinθ

Pythag­orean Identities

 sin²θ + cos²θ = 1 tan²θ + 1 = sec²θ 1 + cos²θ = csc²θ

Double­-Angle Identities

 sin2θ = 2sinθcosθ tan2θ = 2tanθ / 1-tan²θ
cos2θ = cos²θ - sin²θ
cos2θ = 1 - 2sin²θ
cos2θ = 2cos²θ - 1

some more identities

 sin(a+b) = sin(a)­cos(b) + cos(a)­sin(b) sin(a-b) = sin(a)­cos(b) - cos(a)­sin(b) cos(a+b) = cos(a)­cos(b) - sin(a)­sin(b) cos(a-b) = cos(a)­cos(b) + sin(a)­sin(b)
tan(a+b) = tan(a)­+tan(b) / 1-tan(­a)t­an(b)
tan(a-b) = tan(a)­+tan(b) / 1+tan(­a)t­an(b)