Sohcahtoa

Definitions

Just an easy way to remember how Sine, Cosine and Tangent work:

Soh…   (Sine = Opposite / Hypotenuse)

cah…  (Cosine = Adjacent / Hypotenuse)

toa (Tangent = Opposite / Adjacent)

Right Triangle

Firstly, the names Opposite, Adjacent and Hypotenuse come from the right triangle:

Sohcahtoa
  • “Opposite” is opposite to the angle θ
  • “Adjacent” is adjacent (next to) to the angle θ
  • “Hypotenuse” is the longest one

Sine, Cosine, & Tangent

Sine, Cosine, and Tangent are the 3 main functions in trigonometry.

They are often shortened to sin, cos and tan.

The calculation is simply one side of a right angled triangle divided by another side. we just have to know which sides, and that is where “sohcahtoa” helps.

For a triangle with an angle θ , the functions are calculated this way:

Sinesoh…sin(θ) = opposite / hypotenuse
Cosine…cah…cos(θ) = adjacent / hypotenuse
Tangent…toatan(θ) = opposite / adjacent

Example

What are the sine, cosine and tangent of 60° ?

A 60° triangle has a hypotenuse (the longest side) of length 2, an opposite side of length √3 and an adjacent side of 1, like this:

Sohcahtoa Example

Now we know the lengths, we can calculate the functions:

Sinesoh…sin(60o) = √3/2
Cosine…cah…cos(60o) = 1/2
Tangent…toatan(60o) = √3

Learn More

Finding an Angle in a Right Angled Triangle

Solving SAS Triangles

Solving SSA Triangles

Vertical Angles

Algebra Index

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