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urp:trig [2021-10-21] nerf_herder |
urp:trig [2021-10-21] (current) nerf_herder |
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| Line 2: | Line 2: | ||
| transformations of sine or cosine function: | transformations of sine or cosine function: | ||
| - | y = a * sin(k(x - c)) + d | + | y = a * sin(b(x - c)) + d |
| {{:urp:sinewave.jpg?418|Sine Wave Transformations}} | {{:urp:sinewave.jpg?418|Sine Wave Transformations}} | ||
| - | (Graphics from www.Desmos.com, labeling was added) a = amplitude, c = phase shift, d = vertical shift, 2π/k = period | + | (Graphics from www.Desmos.com, labeling was added) a = amplitude, c = phase shift, d = vertical shift, 2π/b = period |
| - | for tan, the period is π/k | + | (for tan the period is π/b) |
| ==== Sin/Cos table ==== | ==== Sin/Cos table ==== | ||
| - | ^ Radians ^ Degrees ^ Cos ^ Sin ^ | + | ^ Radians ^ Degrees ^ Cos ^ Sin ^ |
| - | | 0 | 0 | 1 | 0 | | + | | **0** | 0 | 1 | 0 | |
| - | | π/6 | 30 | √3/2 | 1/2 | | + | | π/6 | 30 | √3/2 | 1/2 | |
| - | | π/4 | 45 | √2/2 | √2/2 | | + | | π/4 | 45 | √2/2 | √2/2 | |
| - | | π/3 | 60 | 1/2 | √3/2 | | + | | π/3 | 60 | 1/2 | √3/2 | |
| - | | π/2 | 90 | 0 | 1 | | + | | **π/2** | 90 | 0 | 1 | |
| - | | 2π/3 | 120 | -1/2 | √3/2 | | + | | 2π/3 | 120 | -1/2 | √3/2 | |
| - | | 3π/4 | 135 | -√2/2 | √2/2 | | + | | 3π/4 | 135 | -√2/2 | √2/2 | |
| - | | 5π/6 | 150 | -√3/2 | 1/2 | | + | | 5π/6 | 150 | -√3/2 | 1/2 | |
| - | | π | 180 | -1 | 0 | | + | | **π** | 180 | -1 | 0 | |
| - | | -5π/6, 7π/6 | 210 | -√3/2 | -1/2 | | + | | -5π/6, 7π/6 | 210 | -√3/2 | -1/2 | |
| - | | -3π/4, 5π/4 | 225 | -√2/2 | -√2/2 | | + | | -3π/4, 5π/4 | 225 | -√2/2 | -√2/2 | |
| - | | -2π/3, 4π/3 | 240 | -1/2 | -√3/2 | | + | | -2π/3, 4π/3 | 240 | -1/2 | -√3/2 | |
| - | | -π/2, 3π/2 | 270 | 0 | -1 | | + | | **-π/2, 3π/2** | 270 | 0 | -1 | |
| - | | -π/3, 5π/3 | 300 | 1/2 | -√3/2 | | + | | -π/3, 5π/3 | 300 | 1/2 | -√3/2 | |
| - | | -π/4, 7π/4 | 315 | √2/2 | -√2/2 | | + | | -π/4, 7π/4 | 315 | √2/2 | -√2/2 | |
| - | | -π/6, 11π/6 | 330 | √3/2 | -1/2 | | + | | -π/6, 11π/6 | 330 | √3/2 | -1/2 | |
| - | | 0, 2π | 360 | 1 | 0 | | + | | **0, 2π** | 360 | 1 | 0 | |
| ==== Conversion Theorems ==== | ==== Conversion Theorems ==== | ||
urp/trig.1634778696.txt.gz · Last modified: 2021-10-21 by nerf_herder
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