Trigonometry

1. 
   
   $$\tan(x)=\frac{\sin(x)}{\cos(x)},\cot(x) = \frac{\cos(x)}{\sin(x)}, \sec(x)=\frac{1}{\cos(x)},\csc(x)=\frac{1}{\sin(x)}.$$
   
   

2. 
   
   $$\sin^2(x)+\cos^2(x)=1, \sec^2(x)=1+\tan^2(x),\csc^2(x)=1+\cot^2(x).$$
   
   

3. 
   
   $$\sin(x + y)=\sin(x)\cos(y)+\cos(x)\sin(y).$$
   
   

4. 
   
   $$\cos(x+y) = \cos(x)\cos(y) - \sin(x)\sin(y).$$
   
   

5. 
   
   $$\tan(x+y) = \frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)}.$$
   
   

6. 
   
   $$\cos(-x)=\cos(x), \sin(-x)=-\sin(x).$$
   
   

7. 
   
   $$\cos(2x)=\cos^2(x)-\sin^2(x)=2\cos^2(x)-1 = 1-2\sin^2(x).$$
   
   

8. 
   
   $$\sin(2x)=2\sin(x)\cos(x).$$
   
   

9. 
   
   $$\cos(\frac{x}{2}) = \pm \sqrt{\frac{1+\cos(x)}{2}}.$$
   
   
   
   
   $$\sin(\frac{x}{2}) = \pm \sqrt{\frac{1-\cos(x)}{2}}.$$
   
   
   The signs need to be fixed by the position of the locator point $P(\frac{t}{2})$.

10. 
    
    $$\frac{\sin(A)}{a}=\frac{\sin(B)}{b} = \frac{\sin(C)}{c} \leqno{\mbox{\bf Sine Law}}.$$
    
    

11. 
    
    $$a^2=b^2+c^2-2bc\cos(A) \leqno{\mbox{\bf Cosine Law}}.$$