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 (Sin/Cos) |
Sec (1/Cos) |
Csc (1/Sin) |
Cot (1/Tan) |
|---|---|---|---|---|---|---|
| 0° | 1 | 0 | 0 | undefined | ||
| 30° | √32 | 12 | 1√3 = √33 | |||
| 45° | √22 | √22 | 1 | |||
| 60° | 12 | √32 | √3 | |||
| 90° | undefined | |||||
| 180° | ||||||
| 270° | ||||||
| 360° |