Title: Math 2250 Background Material
Tags: Identity Trig Geometry Exponential Algebra

Q: [latex]$\sin(a+b)$[/latex]
A: [latex]$\sin a \cos b + \cos a \sin b$[/latex]

Q: [latex]$1 + \tan^2 \theta$[/latex]
A: [latex]$\sec^2 \theta$[/latex]

Q: [latex]$\cos(a+b)$[/latex]
A: [latex]$\cos a \cos b - \sin a \sin b$[/latex]

Q: [latex]$\sin 2\theta$[/latex]
A: [latex]$2 \sin \theta \cos \theta$[/latex]

Q: [latex]$\cos 2\theta$[/latex]
A: [latex]$\cos^2 \theta - \sin^2 \theta$[/latex]

Q: [latex]$\sin^2 \theta$[/latex]
A: [latex]$$\frac{1 - \cos2\theta}{2}$$[/latex]

Q: [latex]$\cos^2 \theta$[/latex]
A: [latex]$$\frac{1 + \cos2\theta}{2}$$[/latex]

Q: [latex]$x^{a+b}$ = [/latex] [...]
A: [latex]$x^{a}x^{b}$[/latex]

Q: [latex]$(x^a)^b$ = [/latex] [...]
A: [latex]$x^{ab}$[/latex]

Q: [latex]$e^{\ln x}=$[/latex]
A: [latex]$x$[/latex]

Q: [latex]$\ln (e^x)$[/latex]
A: [latex]$x$[/latex]

Q: The solutions of [latex]$a x^2 + b x + c = 0$[/latex] are given by [latex]$x = $[/latex]
A: [latex]$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/latex] (quadratic formula)

Q: How to complete the square: [latex]$x^2 + 2 a x + b =$[/latex]
A: [latex]$(x + a)^2 + (b-a^2)$[/latex]

Q: [latex] The distance between $(x_1,y_1)$ and $(x_2,y_2)$ in the plane is [/latex]
A: [latex]$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$[/latex].

Q: [latex] The \textbf{area} of a circle of radius $r$ is [/latex]
A: [latex] $\pi r^2$ [/latex]

Q: [latex] The \textbf{perimeter} of a circle of radius $r$ is [/latex]
A: [latex] $2 \pi r$ [/latex]

Q: [latex] The \emph{volume} of a sphere of radius $r$ is [/latex]
A: [latex]$\frac{4}{3} \pi r^3$[/latex]

Q: [latex] The \textbf{area} of a sphere of radius $r$ is [/latex]
A: [latex] $4 \pi r^2$ [/latex]

Q: [latex] The volume of a cylinder of height $h$ and radius $r$ is [/latex]
A: [latex] $\pi r^2 h$ [/latex]