Advanced Trigonometry
Here's what they taught you in a standard trig class:
| radians | degrees | sin | cos | tan
|
|---|
| 0 | 0 | 0 | 1 | 0
|
| π/6 | 30 | 1 / 2 | √3 / 2 | 1 / √3
|
| π/4 | 45 | 1 / √2 | 1 / √2 | 1
|
| π/3 | 60 | √3 / 2 | 1 / 2 | √3
|
| π/2 | 90 | 1 | 0 | ∞
|
Here's what they didn't teach you, but this definitely comes in handy sometimes, especially if you are dealing with pentagons, octagons, or dodecagons:
| radians | degrees | sin | cos | tan
|
|---|
| π/12 | 15
| (√6 – √2) / 4 | (√6 + √2) / 4 | 2 – √3
|
| π/10 | 18
| (√5 – 1) / 4 | √(10 + 2√5) / 4 | √(1 – 2/√5)
|
| π/8 | 22.5
| (2 – √2) / 2 | (2 + √2) / 2 | √2 – 1
|
| π/5 | 36
| √(10 – 2√5) / 4 | (√5 + 1) / 4 | √(5 – 2√5)
|
| 3π/10 | 54
| (√5 + 1) / 4 | √(10 – 2√5) / 4 | √(1 + 2/√5)
|
| 3π/8 | 67.5
| (2 + √2) / 2 | (2 – √2) / 2 | √2 + 1
|
| 2π/5 | 72
| √(10 + 2√5) / 4 | (√5 – 1) / 4 | √(5 + 2√5)
|
| 5π/12 | 75
| (√6 + √2) / 4 | (√6 – √2) / 4 | 2 + √3
|