Product-to-Sum, Sum-to-Product Formula Fun

Rewrite the expression as a sum or difference:  $\cos2y\ \cdot\sin\ 5y$  

•  $\frac{1}{2}\sin7y+\frac{1}{2}\sin3y$  

•  $\frac{1}{2}\sin7y+\sin3y$  

•  $\frac{1}{2}\sin7y-\frac{1}{2}\sin3y$  

•  $\frac{1}{2}\sin7y-\sin3y$  

Tags

CCSS.HSF.TF.C.9

Find the exact value of the expression: $\sin165\cdot\sin15$  

•  $\frac{\sqrt{3}+2}{2}$  

•  $\frac{-\sqrt{3}+2}{4}$  

•  $\frac{\sqrt{3}-2}{2}$  

•  $\frac{-\sqrt{3}-2}{4}$  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.9

Find the exact value of the expression:  $\frac{4}{3}\left[\sin255+\sin15\right]$  

•  $\frac{-2\sqrt{3}}{2}$  

•  $\frac{2}{3}$  

•  $\frac{2\sqrt{2}}{3}$  

•  $-\frac{2\sqrt{2}}{3}$  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.9

Rewrite the expression as a product:  $\sin4\alpha\cdot\sin8\alpha$  

•  $2\cos6\alpha\sin2\alpha$  

•  $2\cos2\alpha\cdot\sin6\alpha$  

•  $2\sin6\alpha\cdot\cos2\alpha$  

•  $2\sin2\alpha\cdot\sin6\alpha$  

Rewrite the expression in terms with no power greater than 1: $\cos^2x\cdot\csc x-\csc x$  

•  $\frac{-\csc x+\csc x\cos2x}{2}$  

•  $\csc x\sin^2x$  

•  $\frac{\csc x-\csc x\cos2x}{2}$  

•  $\frac{\cos2x-\csc x}{4}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Rewrite the expression in terms with no power greater than 1: $\sin^2\theta\cdot\cos^2\theta$  

•  $\frac{1}{8}-\frac{1}{8}\cos4\theta$  

•  $1-\cos4\theta$  

•  $\cos4\theta-1$  

•  $\frac{-1}{8}+\frac{1}{8}\cos4\theta$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\sin5B\sin B$  

•  $\frac{\cos4B-\cos6B}{2}$  

•  $\frac{\sin4B+\cos6B}{2}$  

•  $\frac{\sin6B+\sin4B}{2}$  

•  $\frac{\cos4B-\sin6B}{2}$  

Tags

CCSS.HSF.TF.C.8

CCSS.HSF.TF.C.9

 $\cos4B\sin B$  

•  $\frac{\sin5B+\cos3B}{2}$  

•  $\frac{\cos5B+\cos3B}{2}$  

•  $\frac{\cos5B+\sin3B}{2}$  

•  $\frac{\sin5B-\sin3B}{2}$  

Tags

CCSS.HSF.TF.C.9

 $\cos57\degree\sin55\degree$  

•  $\frac{\cos112\degree-\cos2\degree}{2}$  

•  $\frac{\sin112\degree-\sin2\degree}{2}$  

•  $\frac{\sin2\degree+\sin112\degree}{2}$  

•  $\frac{\sin112\degree-\cos\ 2\degree}{2}$  

Tags

CCSS.HSF.TF.C.8

CCSS.HSF.TF.C.9

 $\cos5A-\cos A$  

•  $-2\cos3A\cos2A$  

•  $-2\sin3A\sin2A$  

•  $-2\sin3A\cos2A$  

•  $2\sin2A\cos3A$  

Tags

CCSS.HSF.TF.C.9