Trigonometry: Sine. Cosine. Tangent.
Rules for calculating Sine, Cosine or Tangent.
There are three different formulae that you should revise and memorise. These are the formulae for Sine, Cosine and Tangent of an angle in a Right Angled Triangle. There are other formulae that you will need to know for triangles that aren't Right Angled Triangles in other worksheets for this chapter.
First, let's take a look again at a Right Angled Triangle but with a different set of labels for each of the sides:
Calculating unknown values.
When presented with a Right Angled Triangle with missing value for a side or an angle, you can calculate those missing values with the following three formulae:
You will use the Sine, Cosine or Tangent of the missing angle depending on which values you have (or don't have) for the Right Angled Triangle.
Use the Formula for Sine if you know only the values for the Opposite (O) and the Hypotenuse (H) sides.
Use the Formula for Cosine if you know only the values for the Adjacent (A)and the Hypotenuse (H) sides.
Use the Formula for Tangent if you know only the values for the Opposite (O) and the Adjacent (A) sides.
You can transpose the above formulae to calculate the values of a missing side (in a Right Angled Triangle) if you know the angle and at least one other side:
or
or
or
There is a lot to remember here but there are a couple of different ways to memorise the above formulae. My personal favourite is the mantra of SOHCAHTOA (pronounced soh-kahr-toh-er). However, some teachers like to show students the pyramids for the above:
Covering the value that you don't know will give you the formula for calculating it.
Covering the value that you don't know will give you the formula for calculating it.