01.4-ExactVals

Exact Values

In VCE Maths Methods (and Specialist Maths), unless told otherwise, you should always leave your answer as an exact value.

This means you leave your answer without evaluating surds, pi, e, fractions etc.

The most common use for exact values is with trig ratios.

For the standard angles, you only need to remember two values:

  • $\sin(30^\circ ) = \dfrac{1}{2}$
  • $\tan(45^\circ ) = 1$

From these two values, we can construct two triangles

01.3exacttriangles1.gif

and fill in the other values using Pythagoras:

01.3exacttriangles2.gif

Then from these triangles we can use SOHCAHTOA to obtain the needed exact values:

01.3exactvals.GIF

You should also know the exact values for 0 and 90.
These can be deduced by remembering the unit circle definitions and that

  • $x = \cos(\theta)$
  • $y = \sin(\theta)$
  • and $\tan(\theta)$ is the y-coordinate on the tangent line x = 1
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