Math 26 Formulas

Velocity

$Radius\cdot\frac{\theta}{t}$ where theta is an angle.

Linear speed

$$\frac{s}{t}\ldots\frac{\theta}{t}$$

Area of a sector

$\frac12r^2\theta$ where theta is in radian.

Arc length

$$S=r\theta$$

Coterminal angles

$$\pm360\degree\ldots\pm2\pi$$

complementary angles

$$\theta a+\theta b=90\degree$$

complementary functions

$$\sin\theta=\cos\left(90-\theta\right)\ldots\tan\theta=\cot\left(90-\theta\right)\ldots\csc\theta=\sec\left(90-\theta\right)$$

Supplementary angles

$$\theta a+\theta b=180\degree$$

DMS

Degrees, Minutes, Seconds

$$\sin2\theta$$

$$2\sin\theta\cos\theta$$

$$\cos2\theta$$

$\cos^2\theta-\sin^2\theta\ldots1-2\sin^2\theta\ldots2\cos^2\theta-1$ $$

$$\tan2\theta$$

$$\frac{2\tan\theta}{1-\tan^2\theta}$$

$$cos\left(A+B\right)$$

$$cosA\cos B-\sin A\sin B$$

$$\cos\left(A-B\right)$$

$$\cos A\cos B+\sin A\sin B$$

$$\sin\left(A+B\right)$$

$$\cos A\sin B+\sin A\cos B$$

$$\sin\left(A-B\right)$$

$$\cos A\sin B-\sin B\cos A$$

$$\tan\left(A+B\right)$$

$$\frac{\tan A+\tan B}{1-\tan A\tan B}$$

$$\tan\left(A-B\right)$$

$$\frac{\tan A-\tan B}{1+\tan A\tan B}$$

Law of sines

Used for SSA and AAS triangles

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

Law of cosines

Used for SAS and SSS

$$a^2=b^2+c^2-2bc\cos A$$

No triangles

$$\sin B>1$$

one triangle

$$\sin B=1$$

1 triangle

$$\sin B\left(a>b\right)$$

two triangles

$$\sin B<1\ldots\left(a<b\right)$$

Area of a SAS triangle

$$A=\frac12bc\sin A$$

Area of a SSS triangle

$$k=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$$

$$s=\frac{a+b+c}{2}$$

Period for cos & sin

$$\frac{2\pi}{b}$$

Period for tan & cot

$$\frac{\pi}{b}$$

phase shift

$$\frac{\theta}{b}$$

starting point

$$bx-\theta$$

vertical shift

c