Precalc 12/4

x | y = tan(x) |
|---|---|
| -π/2 | Undefined (Vertical Asymptote) |
| -π/4 | -1 |
| 0 | 0 |
| π/4 | 1 |
| π/2 | Undefined (Vertical Asymptote) |

| x | cot(x) |
|---|---|
| 0 | undefined (vertical asymptote) |
| π/4 | 1 |
| π/2 | 0 |
| 3π/4 | -1 |
| π | Undefined (vertical asymptote) |

| x | cos(x) |
|---|---|
| 0 | 1 |
| π/2 | 0 |
| π | -1 |
| 3π/2 | 0 |
| 2π | 1 |

| x | sin(x) |
|---|---|
| 0 | 0 |
| π/2 | 1 |
| π | 0 |
| 3π/2 | -1 |
| 2π | 0 |

Sin x starts at 0

Cos x starts at 1

For asinx + bcosx the amplitude is the square root of (a² plus b²)

asinx + bcosx = square root of (a² + b²) times sin(x plus theta)

asinx + bcosx = square root of (a² + b²) times cos(x minus theta)

w/2pi is equal to frequency

2pi/w is equal to period

1/period = frequency

example of ln( is ln(e^5x) = 5x.

Another example of ln( is ln(e^-2x) = -2x

y = k times (e^-ct) times (sin(wt)) or y = k times (e^-ct) times (cos(wt))

where c is the damping constant, k is the initial amplitude and a(t) aka the amplitude is equal to k times (e^-ct)

Cos and secant are even functions so they reflect across the y-axis

The rest of the trig functions (ones that aren’t cos and sec) are odd and reflect across the origin.