Trig - Sum and Difference

Which of the following is equivalent to  $\sin\left(\alpha+\beta\right)$  ?

•  $\sin\alpha\cos\alpha+\sin\beta\cos\beta$  

•  $\sin\alpha\cos\alpha-\sin\beta\cos\beta$  

•  $\sin\alpha\cos\beta+\cos\alpha\sin\beta$  

•  $\sin\alpha\cos\beta-\cos\alpha\sin\beta$  

Which of the following is equivalent to  $\cos\left(\alpha-\beta\right)$  ?

•  $\cos\alpha\cos\beta+\sin\alpha\sin\beta$  

•  $\cos\alpha\cos\beta-\sin\alpha\sin B$  

•  $\cos\alpha\sin\beta+\sin\alpha\cos\beta$  

•  $\cos\alpha\sin\beta-\sin\alpha\cos\beta$  

Which of the following is equivalent to  $\tan\left(\alpha+\beta\right)$  ?

•  $\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}$  

•  $\frac{\tan\alpha-\tan\beta}{1-\tan\alpha\tan\beta}$  

•  $\frac{\tan\alpha+\tan\beta}{1+\tan\alpha\tan\beta}$  

•  $\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$  

Find the exact value of  $\sin105\degree$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

•  $\frac{\sqrt{6}+\sqrt{2}}{4}$  

•  $\frac{\sqrt{3}+1}{2}$  

 $\cos105\degree$  

•  $\frac{\sqrt{2}+\sqrt{6}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{1-\sqrt{3}}{2}$  

 $\tan105\degree$  

•  $2-\sqrt{3}$  

•  $2+\sqrt{3}$  

•  $-2-\sqrt{3}$  

•  $-2+\sqrt{3}$  

If  $\sin\alpha=\frac{5}{13}$  and  $\cos\beta=\frac{4}{5}$  (both in QI), then find  $\sin\left(\alpha-\beta\right)$  

•  $\frac{16}{65}$  

•  $-\frac{16}{65}$  

•  $\frac{65}{16}$  

•  $-\frac{65}{16}$  

If  $\sin\alpha=\frac{5}{13}$  and  $\cos\beta=\frac{4}{5}$  (both in QI), find  $\cos\left(\alpha+\beta\right)$  

•  $\frac{33}{65}$  

•  $-\frac{33}{65}$  

•  $\frac{63}{65}$  

•  $-\frac{63}{65}$  

If  $\sin\alpha=\frac{5}{13}$  and  $\cos\beta=\frac{4}{5}$  (both in QI), find  $\tan\left(\alpha-\beta\right)$  

•  $\frac{16}{63}$  

•  $-\frac{16}{63}$  

•  $\frac{63}{16}$  

•  $-\frac{63}{16}$  

If the 2 legs of a right triangle are 7 in. and 24 in., how long is the hypotenuse?

• 31 in.

• 17 in.
  

• $\sqrt{527}\$ in.

• 25 in.