Applying Sum and Difference Identities

If  $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$   $and\ \angle A\ and\ \angle B$  are acute angles, what is the value of  $\cos\left(A-B\right)?$  

•  $-\frac{2}{3}$  

•  $\frac{4\sqrt{5}-6}{15}$  

•  $\frac{4\sqrt{5}+2}{5}$  

•  $\frac{4\sqrt{5}+6}{15}$  

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

Given $\tan A=\frac{2}{3}and\ \tan B=\frac{1}{2},\$ where  $\angle A\ and\ \angle B\ in\ quadrant\ I$   $Evaluate\ \tan\left(A+B\right)$  

•  $\frac{1}{8}$  

•  $\frac{7}{8}$  

•  $\frac{1}{4}$  

•  $\frac{7}{4}$  

Tags

CCSS.HSG.SRT.C.8

Given angle A and B in Quadrant I with  $\sin A\ =\frac{12}{13}\ and\ \cos B\ =\frac{3}{5}\ find\ \cos\left(A+B\right)$  

•  $-\frac{33}{65}$  

•  $\frac{33}{65}$  

•  $\frac{1}{2}$  

•  $\frac{12}{13}$  

Tags

CCSS.HSF.TF.C.9

 $\sin A=\ \frac{12}{13\ }\ and\ \cos B=\ \frac{4}{5},\ find\ \cos\left(A+B\right)$  Given angle A and B in Quadrant I with

•  $\frac{16}{45}$  

•  $\frac{16}{65}$  

•  $\frac{36}{65}$  

•  $\frac{20}{45}$  

Tags

CCSS.HSF.TF.C.9

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$  what is the value of  $\tan\left(A+B\right)?$  

•  $\frac{1}{8}$  

•  $\frac{7}{8}$  

•  $\frac{1}{4}$  

•  $\frac{7}{4}$  

Tags

CCSS.HSF.TF.C.9

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$  and A and B are first quadrant angles, what is the value of  $\sin\left(A+B\right)$  ?

•  $\frac{63}{65}$  

•  $-\frac{33}{65}$  

•  $\frac{33}{65}$  

•  $-\frac{63}{65}$  

Tags

CCSS.HSF.TF.C.9