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Trigonometry Year 10 Cheat Sheet by

Covers: Trigonometric Functions, Similarity Test for Similar Triangles, Scale Factor, Pythagoras Theorem, Pythagoras in 3 Dimensions, How to find a Right-Angled Triangle, Bearings

Trigon­ometric Functions

*adjacent and opposite labels can change depending on the angle being found

Pythagoras Theorem

c2 = a2 + b2
c = √a2 + b2
a2 = c2 - b2
a = √c2 - b2
b2 = c2 - a2
b = √c2 - a2
c is the hypotenuse whereas a and b can be switched interc­han­geably

Pythagoras in 3 Dimensions

The Pythag­orean Theorem can also be used in three dimensions to find the diagonal length of a rectan­gular prism
d = √x2 + y2 + z2

Finding right angles in general shapes

Example X

True Bearings


Similarity Test for Similar Triangles

Scale Factor

Scale factor is the ratio between the scale of a given original object and a new object, which is its repres­ent­ation but of a different size (bigger or smaller).
sf = larger figure dimensions ÷ smaller figure dimensions

Example of Scale Factor

Example of Inverse

Conven­tional Bearings


Examples of Trigon­ometric functions

Examples of Angles

Corres­pon­ding: Equal the same
Alternate: Equals 180

Examples of Similar Triangles



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