AP Pre-Calculus Formula Sheet 1 Notes

Trigonometric Functions

• $\sin \Theta = \frac{y}{r}$

• $\cos \Theta = \frac{x}{r}$

• $\tan \Theta = \frac{y}{x}$

• $\csc \Theta = \frac{r}{y}$

• $\sec \Theta = \frac{r}{x}$

• $\cot \Theta = \frac{x}{y}$

Finding Coordinates with Radius and Radians

• To find the x-coordinate given the radius and radians: $x = r \cos \Theta$

• To find the y-coordinate given the radius and radians: $y = r \sin \Theta$

Midline and Amplitude

• Midline: $y = \frac{max + min}{2}$

• Amplitude: $x = \frac{max - min}{2}$

Period of a Function

• Period: Length of one complete repetition of the function's cycle.

Arc Length

• Arc Length: $s = r\theta$, where:

  • $s$ = arc length

  • $r$ = radius

  • $\theta$ = theta in radians

Converting Between Radians and Degrees

• Radians to Degrees: $x * \frac{180}{\pi}$

• Degrees to Radians: $x * \frac{\pi}{180}$

Angles with the Same Trigonometric Values

• Angle with the same sine: add to 180.

• Angle with the same cosine: add to 360.

• Angle with the same tangent: 180 apart.

Polar Form

• $x = r \cos \theta$

• $y = r \sin \theta$

Sinusoidal Function

• $y = A \sin(B(t-h)) + K$, where:

  • $A$ = Amplitude

  • $B$ = Horizontal Stretch

  • Period = $\frac{2\pi}{B}$

  • $h$ = Horizontal Shift

  • $K$ = Vertical Shift / Midline

  • $t$ = theta/angle