Quiz 11 Practice: Sum and Difference Identities

Which of the following is the same as  $\cos\ \left(A+B\right)$  

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

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

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

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

Tags

CCSS.HSF.TF.C.9

Which of the following is equivalent to  $\tan\ \left(A-B\right)$  

•  $\tan\ A\ -\ \tan\ B$  

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

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

•  $\frac{\sin\ A}{\cos\ B}$  

Tags

CCSS.HSF.TF.C.9

Expand  $\sin\ \left(33^{o\ }+42^o\right)$  

•  $\sin\ 75^{o\ }$  

•  $\sin\ 33^o\cos42^o+\cos33^o\sin42^o$  

•  $\sin\ 33^o\cos42^o-\cos33^o\sin42^o$  

•  $\cos33^o\cos42^o+\sin33^o\sin42^o$  

Tags

CCSS.HSF.TF.C.9

Expand  $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$  

•  $\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$  

•  $\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$  

•  $\cos\ \frac{2\pi}{11}$  

•  $\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$  

Tags

CCSS.HSF.TF.C.9

Use sum or difference angles identity to find the exact value for  $\cos105^o$  

•  $\frac{\sqrt{6}+\sqrt{2}}{4}$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{-\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

Tags

CCSS.HSF.TF.C.9

Use sum or difference angles identity to find the exact value for       $\sin\ \left(-15^o\right)$  

•  $\frac{\sqrt{6}+\sqrt{2}}{4}$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

•  $-\frac{\sqrt{3}}{2}$  

Tags

CCSS.HSF.TF.C.9

Given  $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$  where  $x\ and\ y$  are both in first quadrant.   $Evaluate\ \sin\left(x+y\right)$  

•  $\frac{3\sqrt{5}+8}{15}$  

•  $\frac{4\sqrt{5}+6}{15}$  

•  $\frac{2\sqrt{5}+12}{15}$  

•  $\frac{4\sqrt{5}+2}{5}$  

Tags

CCSS.HSF.TF.C.9

Find the exact value of the expression.
cos(20)cos(40) - sin(20)sin(40)

• 1/4
• 1/2
• √(3)/2
• √(3)

Tags

CCSS.HSF.TF.C.9

Please choose the correct sum and difference formula:
cos (α-β) =

• sin α cos β + cos α sin β
• sin α cos β - cos α sin β
• cos α cos β - sin α sin β
• cos α cos β + sin α sin β

Tags

CCSS.HSF.TF.C.9

Expand and simplify    $\tan\ \left(x+\frac{\pi}{4}\right)$  

•  $\tan\ x+1$  

•  $\tan x-1$  

•  $\frac{\tan\ x+1}{1-\tan x}$  

•  $\frac{\tan x-1}{1+\tan x}$  

Tags

CCSS.HSF.TF.C.9