06Atrigrules

toc = Basic Trigonometry Rules =

SOHCAHTOA
We define any right-angled triangle, with an angle as: (OPP → Opposite, ADJ → Adjacent, HYP → Hypotenuse) Then, by similar triangles, compared to the triangle from the unit circle, we get:

math \dfrac{\sin(\theta)}{1} = \dfrac{\text{OPP}}{\text{HYP}} \quad \text{ or } \quad \sin(\theta) = \dfrac{\text{OPP}}{\text{HYP}} math

AND

math \dfrac{\cos(\theta)}{1} = \dfrac{\text{ADJ}}{\text{HYP}} \quad \text{ or } \quad \cos(\theta) = \dfrac{\text{ADJ}}{\text{HYP}} math

Also by similar triangles:

math \dfrac{\tan(\theta)}{1} = \dfrac{\text{OPP}}{\text{ADJ}} \quad \text{ or } \quad \tan(\theta) = \dfrac{\text{OPP}}{\text{ADJ}} math

Thus we obtain the three basic rules of trigonometry. Many people remember these using the SOH-CAH-TOA mnemonic.

For examples of solving right-angled triangles, go here:
 * Using Trigonometry to find side lengths
 * Using Trigonometry to find angles

Tangent Identity Also by similar triangles:

math \dfrac{\tan(\theta)}{1} = \dfrac{\sin(\theta)}{\cos(\theta)} math

which gives us: This is known as the Tangent Identity

Pythagorean Identity
If we apply Pythagoras' Theorem to the triangle from the unit circle, we get: This is known as the Pythagorean Identity

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