SUVAT equations

  1. \hspace{10pt}V=U+AT
  2. \hspace{10pt}S=\left(\frac{U+V}{2}\right)T
  3. \hspace{10pt}V^2=U^2+2AS
  4. \hspace{10pt}S=UT+\frac{1}{2}AT^2
  5. \hspace{10pt}S=VT-\frac{1}{2}AT^2

where

Variable Description SI unit
S displacement m (metres)
U initial velocity m/s (metres per second)
V final velocity m/s (metres per second)
A acceleration 9.8 m/s/s (metres per second per second)
T total time s (seconds)

 
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Trigonometric Identities

Fundamental Formulae

\frac{\sin(\theta)}{\cos(\theta)}=\tan(\theta)

\cos^2(\theta)+\sin^2(\theta)=1

Double Angle Formulae

\sin(2\theta)=2\sin(\theta)\cos(\theta)

\cos(2\theta)=\cos(\theta)^2-\sin^2(\theta)
\cos(2\theta)=2\cos^2(\theta)-1
\cos(2\theta)=1-2\sin^2(\theta)

Compound Angle Formulae

\sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)

\cos(\alpha\pm\beta)=\sin(\alpha)\sin(\beta)\mp\cos(\alpha)\cos(\beta)
\tan(\alpha\pm\beta)=\frac{\tan(\alpha)\pm\tan(\beta)}{1\mp\tan(\alpha)\tan(\beta)}

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Transformations

A y-transformation affects the y coordinates of a curve. You can identify a y-transformation as changes are made outside the brackets of y=f(x).

  • f(x)\rightarrow f(x)+4, this is a shift in y, the x coordinates are unaffected but all the y coordinates go up by 4.
  • f(x)\rightarrow f(x)-3, this is a shift in y, the x coordinates are unaffected but all the y coordinates go down by 3.
  • f(x)\rightarrow 2f(x), this is a stretch in y, the x coordinates are unaffected but all the y coordinates are doubled.
  • f(x)\rightarrow -f(x), this is a flip in y, the x coordinates are unaffected but all the y coordinates are flipped across the x-axis.

x-transformations

x-transformations always behave in the opposite way to what is expected. They can be identified when changes are made inside the brackets of y=f(x).

  • f(x)\rightarrow f(x+4), this is a shift in the x direction, the y coordinates are unaffected but all the x coordinates go to the left by 4, the opposite direction to what is expected.
  • f(x)\rightarrow f(x-3), this is a shift in the x direction, the y coordinates are unaffected but all the x coordinates go to the right by 3, the opposite direction to what is expected.
  • f(x)\rightarrow f(2x), this is a stretch in the x direction, the y coordinates are unaffected but all the x coordinates are halved, the opposite to what is expected.
  • f(x)\rightarrow f(-x), this is a flip in the x direction, the y coordinates are unaffected but all the x coordinates are flipped across the y-axis.

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