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Interactive trig functions app
Interactive circle, trig, radians, arc length app
Interactive Laws of sines and cosines app
SOH CAH TOA:
If know distance adj to pole, tower, etc. and angle a to top of the pole,
then the height opp of the pole is adj · tan a and
the dsitance hyp to top of pole is adj · sec a
If know distances adj to pole, tower, etc. and hyp to top of pole
then the height opp of the pole is adj · tan(arccos(a/hyp))
The co- functions are the corresponding trig function of the complement of the angle:
cos(a) = sin(90-a)
cot(a) = tan(90-a)
csc(a) = sec(90-a)
sine is the fundamental function, all others can be drefined in terms of it:
cos(x) = sin(x+π/2)
360° / 2π radians = ~57° / 1 radian
Unit circle: center angle in radians equals arc length
Unit circle: sector of central angle 1 radian has area 1/2
| Degrees ° | a Radians | x = cos a | y = sin a | x2+y2=1 | slope of tangent line = - 1 / tan a = -cot a |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 1+0 | ∞ |
| ~14.47 | ~.2527 | √15/4 ≈.968 | 1/4=.25 | 15/16+1/16 | -√15 ≈-3.873 |
| 15 | π/12 ≈ .2618 | (√6+√2)/4≈.966 | (√6-√2)/4≈.258 | .933+.0667 | -(2+√3) ≈-3.732 |
| 30 | π/6 ≈ .5235 | √3/2 ≈.866 | 1/2=.5 | 3/4+1/4 | -√3 ≈-1.732 |
| ~35.26 | ~.6155 | √2/√3 ≈.816 | 1/√3 ≈.577 | 2/3+1/3 | -√2 ≈-1.414 |
| 45 | π/4 ≈ .7853 | √2/2 ≈.707 | √2/2 ≈.707 | 1/2+1/2 | -1 |
| ~54.74 | ~.9553 | 1/√3 ≈.577 | √2/√3 ≈.816 | 1/3+2/3 | -1/√2 ≈-.707 |
| ~57.29 | 1 | ~.5403 | ~.8414 | .2919+.7079 | ~-.642 |
| 60 | π/3 ≈ 1.047 | 1/2=.5 | √3/2 ≈.866 | 1/4+3/4 | -1/√3 ≈-.577 |
| 75 | 5π/12 ≈ 1.309 | (√6-√2)/4 ≈ .2588 | (√6+√2)/4 ≈ .966 | .067+.933 | -(2-√3) ≈-.268 |
| ~75.52 | ~1.318 | 1/4=.25 | √15/4 ≈.968 | 1/16+15/16 | -1/√15 ≈-.258 |
| 90 | π/2 ≈ 1.571 | 0 | 1 | 0+1 | 0 |
| 0° | 15° | 30° | 45° | 60° | 75° | 90° | |
| sine | 0 | .258 | .5 | .707 | .866 | .968 | 1 |
|---|---|---|---|---|---|---|---|
| Δ | .258 | .244 | .207 | .159 | .104 | .032 |
First and second derivatives of sine function:
First and second derivatives of tan function:
hyperbolic sin and hyperbolic cos:
