Math Review

Everybody should know this sort of thing (and more, but certainly this).

1. Trigonometry

   

   
   

   $$\sin(\theta) =$$
   
   
   
   
   $$\cos(\theta) =$$
   
   
   
   
   $$\tan(\theta) =$$
   
   

2. 
   
   $$\int \sin(\theta) d\theta =$$
   
   

3. Solve for $x$:

   
   

   $$5x + 5y = 10$$
   
   
   
   
   $$5x - 2z = 4$$
   
   
   
   
   $$2z - y = 0$$
   
   

4. 
   
   $$\frac{d }{dt} (at^5 + be^{-c t^2} + sin(dt)) =$$
   
   

5. Solve for x:
   
   $$ax^2 + bx + c = 0$$
   
   

6. Cross product (give magnitude and direction)
   
   $$\vec{A} \times \vec{B} =$$
   
   

7. Dot product
   
   $$\vec{A} \cdot \vec{B} =$$
   
   

8. Binomial expansion (I'm just giving you this because I think it is immensely useful for understanding things like tides, which are the difference between two almost equal reciprocal powers).
   
   $$(1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \ldots$$
   
   

   (Note that this converges for $\vert x\vert < 1$ only, which dictates the algebra used in its typical application. Well worth learning for next semester, if nothing else.)