Activity: Trig Reciprocals

You know about Sine, Cosine and Tangent, right?

And the Unit Circle helps get us these important angles:

Angle Cos Sin Tan
=Sin/Cos
30° √32 12 1√3 = √33
45° √22 √22 1
60° 12 √32 √3

But now let's try for more!

First we extend this table to have more angles

Then we add Cosecant, Secant, and Cotangent, which are each a "flip" (reciprocal) of sin, cos and tan.

The Challenge

Now it is your turn, see if you can complete the table below:

Angle Cos Sin Tan
(SinCos)		 Sec
(1Cos)		 Csc
(1Sin)		 Cot
(CosSin or 1Tan)
0° 1 0 0 undefined
30° √32 12 1√3 = √33
45° √22 √22 1
60° 12 √32 √3
90° undefined
180°
270°
360°

Watch out: It is easy to mix up Secant and Cosecant

A helpful trick: each pair of reciprocals has exactly one "co-":

  • Sine goes with Cosecant: 1sin
  • Cosine goes with Secant: 1cos
  • Tangent goes with Cotangent: 1tan
Unit Circle Sine, Cosine and Tangent Activity Index