Math 122 Formula Sheet

Math 122 Formula Sheet

\sin (x \pm y) = \sin x \cos y \pm \cos x \sin y

\cos (x \pm y) = \cos x \cos y \mp \sin x \sin y

\sin (\frac{u}{2}) = \pm \sqrt{\frac{1 - \cos u}{2}}

\cos (\frac{u}{2}) = \pm \sqrt{\frac{1 + \cos u}{2}}

\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

c^{2} = a^{2} + b^{2} - 2 a b \cos C

, etc.

u \cdot v = | u | | v | \cos θ

S_{n} = n (\frac{a_{1} + a_{n}}{2})

S_{n} = a_{1} (\frac{1 - r^{n}}{1 - r})

S = \frac{a}{1 - r}

{(a + b)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) a^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a^{n - 1} b + (\begin{matrix} n \\ 2 \end{matrix}) a^{n - 2} b^{2} + \dots + (\begin{matrix} n \\ n - 1 \end{matrix}) a b^{n - 1} + (\begin{matrix} n \\ n \end{matrix}) b^{n}

Circle

{(x - h)}^{2} + {(y - k)}^{2} = r^{2}

Parabola

{(y - k)}^{2} = 4 p (x - h)

Parabola opening horizontally with vertex at the point (h, k).

{(x - h)}^{2} = 4 p (y - k)

Parabola opening vertically with vertex at the point (h, k).

Ellipse

\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1

\frac{{(x - h)}^{2}}{b^{2}} + \frac{{(y - k)}^{2}}{a^{2}} = 1

Hyperbola

\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1

Hyperbola opening horizontally with center at the point (h, k).

\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1

Hyperbola opening vertically with center at the point (h, k).