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Trigonometry cheat sheet

All 9 formulas on one page. Print it or save it as a PDF; it fits on 2 sides of A4 or Letter.

SOH CAH TOA (right-triangle trigonometry)

sin⁡θ=oppositehypotenuse, cos⁡θ=adjacenthypotenuse, tan⁡θ=oppositeadjacent
  • θ one of the two acute angles (not the right angle)
  • o the opposite side: across the triangle from θ
  • a the adjacent side: next to θ, but not the hypotenuse
  • h the hypotenuse: the longest side, opposite the right angle

Pythagorean identity

sin2⁡θ+cos2⁡θ=1
Divided by cos²θtan2⁡θ+1=sec2⁡θ
Divided by sin²θ1+cot2⁡θ=csc2⁡θ
  • sin⁡θ the sine of the angle (between −1 and 1)
  • cos⁡θ the cosine of the angle (between −1 and 1)
  • θ any angle

Double-angle formulas

sin⁡2θ=2sin⁡θcos⁡θ, cos⁡2θ=cos2⁡θ−sin2⁡θ
Cosine, using only sinecos⁡2θ=1−2sin2⁡θ
Cosine, using only cosinecos⁡2θ=2cos2⁡θ−1
Tangenttan⁡2θ=2tan⁡θ1−tan2⁡θ
  • θ the angle
  • sin⁡(2θ) the sine of the doubled angle
  • cos⁡(2θ) the cosine of the doubled angle

Angle sum and difference formulas

sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B, cos⁡(A±B)=cos⁡Acos⁡B∓sin⁡Asin⁡B
Tangenttan⁡(A±B)=tan⁡A±tan⁡B1∓tan⁡Atan⁡B
  • A the first angle
  • B the second angle
  • sin⁡(A+B) the sine of the sum A + B
  • cos⁡(A+B) the cosine of the sum A + B
  • ∓ "minus or plus": the opposite sign to the ± on the left

Law of sines

asin⁡A=bsin⁡B=csin⁡C
  • a the side opposite angle A
  • A the angle opposite side a
  • b the side opposite angle B
  • B the angle opposite side b
  • c the third side, opposite angle C

Law of cosines

c2=a2+b2−2abcos⁡C
Solved for the anglecos⁡C=a2+b2−c22ab
  • c the side opposite angle C
  • a one side next to angle C
  • b the other side next to angle C
  • C the angle between sides a and b

Area of a triangle from two sides and an angle

A=12absin⁡C
  • A the area of the triangle (A)
  • a one side
  • b another side
  • C the angle between sides a and b

Degrees and radians

radians=degrees×π180
Radians to degreesdegrees=radians×180π
One radian1 rad≈57.2958°
  • r the angle in radians
  • d the angle in degrees
  • π pi, about 3.14159

Sine wave (amplitude, period and phase)

y=Asin⁡(B(x−C))+D
PeriodP=360°|B|=2π|B|rad
RangeD−|A|≤y≤D+|A|
  • y the height of the wave at x
  • A the amplitude: half the distance from trough to peak (a negative A flips the wave)
  • B the frequency factor: one cycle takes 360°/|B| (or 2π/|B| radians)
  • C the phase shift: the wave is moved C to the right
  • D the vertical shift: the midline is y = D
  • x the input (an angle, or time)

letx.io · Trigonometry cheat sheet · 2026-10-31