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.HSG.SRT.C.7

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.HSG.SRT.C.7

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.HSG.SRT.C.7

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.HSG.SRT.C.8

 $\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$  is equivalent to

•  $\sin\ 90^{o\ }$  

•  $\sin\ 60^{o\ }$  

•  $\cos\ 90^{o\ }$  

•  $\cos\ 60^{o\ }$  

Tags

CCSS.HSF.TF.C.9

 $\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$  is equivalent to

•  $\tan75^o$  

•  $\tan\ 15^o$  

•  $\frac{\sin45^o}{\cos30^o}$  

•  $\tan90^{o\ }$  

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

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

• sin(120)
• cos(120)
• cos(230)
• sin(230)

Tags

CCSS.HSF.TF.C.9