 # Trigonometry

Trigonometry is the study of triangles which connects sides to angles. It uses functions called the sine, cosine and tangent. You can find these on scientific calculators with buttons named sin, cos and tan.

Use the phrase SOHCAHTOA to help you remember how to use trigonometry:
SOH = Sin x = Opposite/Hypotenuse
CAH = Cos x = Adjacent/Hypotenuse
TOA = Tan x = Opposite/Adjacent

The most common use for these functions is to find sides and angles of a right angled triangle. The rules follow:

The sides and angles of a non-right-angled triangle can also be found using the following rules:

The functions all give graphs which are important. You should know how to sketch them all and know how to use them.

The Sine Curve

The Cosine Curve

The Tan Curve

From the curves we can see there is always more than one possible value for any number you are working out the inverse of ( sin-1 0.5 = 30° or 150° ). The problem is that your calculator only gives you one of the values ( the one below 90° ). You must remember the curves to find the position of the second angle.

Shape and Space

Shape and Space

Shape and Space

Shape and Space

Shape and Space

Shape and Space