MAT101 Formulas

sin(θ) = Opp / Hyp

used to find angles or sides when you have opposite + hypotenuse

cos(θ) = Adj / Hyp

used to find angles or sides when you have adjacent + hypotenuse

tan(θ) = Opp / Adj

used to find angles or sides when you have opposite + adjacent

θ = sin⁻¹(Opp/Hyp)

used to find an angle from opposite + hypotenuse

θ = cos⁻¹(Adj/Hyp)

used to find an angle from adjacent + hypotenuse

θ = tan⁻¹(Opp/Adj)

used to find an angle from opposite + adjacent

Opposite = across from the angle

used to correctly label triangle sides (O)

Adjacent = next to the angle

used to correctly label triangle sides (A)

Hypotenuse = longest side

used to correctly label triangle sides (H)

a² + b² = c²

used to find a missing side when no angle is given (Pythagoras)

speed = distance ÷ time

used for rate problems

distance = speed × time

used for travel problems

time = distance ÷ speed

used for timing problems

unit rate = total ÷ number

used to compare deals or prices

percentage = (part ÷ whole) × 100

used to find percent

part = (percentage ÷ 100) × whole

used to find the amount

percentage change = (difference ÷ original) × 100

used for increase/decrease

multiplier = 1 + (percentage ÷ 100)

used for percentage increase

multiplier = 1 − (percentage ÷ 100)

used for percentage decrease

new value = original × multiplier

used for repeated percentage changes

m = (change in y) ÷ (change in x)

used to find gradient

y = mx + c

used to write a straight‑line equation

c = y‑intercept

used to find where the graph crosses the y‑axis

Area = length × width

used for rectangles

Area = ½ × base × height

used for triangles

Area = πr²

used for circles

Circumference = 2πr

used for circles

Perimeter = sum of all sides

used for any shape

Volume = length × width × height

used for cuboids

Volume = area of base × height

used for prisms

Density = mass ÷ volume

used for density problems

Mass = density × volume

used for finding mass

Volume = mass ÷ density

used for finding volume

1 tonne = 1000 kg

used for truck/weight problems