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Trigonometry Identities - Product to Sum to Identity (Radians)

Level 1

This math topic focuses on practicing trigonometric identities, specifically the conversion from product to sum formulas involving angles expressed in radians. Students are expected to complete the transformation of a product of cosine and sine functions into a sum or difference of trigonometric functions. Each problem provides an expression involving trigonometric terms with angles in radians, and students are tasked with converting these expressions using product to sum identities. This not only reinforces their understanding of trigonometric relationships but also improves their manipulation and simplification skills with trigonometric expressions in radians.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry Identities - Product to Sum to Identity (Radians) Worksheet

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Trigonometry Identities - Product to Sum to Identity (Radians)
1
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(Pi over 4 )}\text{cos}{(5Pi over 3 )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(Pi over 4 + 5Pi over 3 ) + \text{cos} to the power of 2 (Pi over 4 + 5Pi over 3 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(Pi over 4 - 5Pi over 3 ) + \text{cos}(Pi over 4 + 5Pi over 3 ) \right]
2
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(Pi over 6 )}\text{sin}{(5Pi over 4 )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(Pi over 6 + 5Pi over 4 ) + \text{sin}(Pi over 6 - 5Pi over 4 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(Pi over 6 + 5Pi over 4 ) - \text{sin}(Pi over 6 - 5Pi over 4 ) \right]
3
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(2Pi over 3 )}\text{sin}{(5Pi over 6 )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(2Pi over 3 + 5Pi over 6 ) - \text{sin}(2Pi over 3 - 5Pi over 6 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(2Pi over 3 + 5Pi over 6 ) + \text{sin}(2Pi over 3 - 5Pi over 6 ) \right]
4
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(7Pi over 6 )}\text{sin}{(Pi over 4 )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(7Pi over 6 + Pi over 4 ) + \text{sin}(7Pi over 6 - Pi over 4 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(7Pi over 6 + Pi over 4 ) - \text{sin}(7Pi over 6 - Pi over 4 ) \right]
5
Complete the product to sum identity for this expression
A LaTex expression showing \text{sin}{(5Pi over 6 )}\text{sin}{(Pi over 4 )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(5Pi over 6 + Pi over 4 ) + \text{sin}(5Pi over 6 + Pi over 4 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(5Pi over 6 - Pi over 4 ) - \text{cos}(5Pi over 6 + Pi over 4 ) \right]
6
Complete the product to sum identity for this expression
A LaTex expression showing \text{sin}{(7Pi over 4 )}\text{cos}{(2Pi over 3 )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(7Pi over 4 + 2Pi over 3 ) + \text{sin}(7Pi over 4 + 2Pi over 3 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(7Pi over 4 + 2Pi over 3 ) + \text{sin}(7Pi over 4 - 2Pi over 3 ) \right]
7
Complete the product to sum identity for this expression
A LaTex expression showing \text{sin}{(5Pi over 4 )}\text{sin}{(11Pi over 6 )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(5Pi over 4 - 11Pi over 6 ) - \text{cos}(5Pi over 4 + 11Pi over 6 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(5Pi over 4 + 11Pi over 6 ) + \text{sin}(5Pi over 4 + 11Pi over 6 ) \right]
8
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(5Pi over 6 )}\text{cos}{(5Pi over 4 )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(5Pi over 6 + 5Pi over 4 ) + \text{sin}(5Pi over 6 - 5Pi over 4 ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(5Pi over 6 - 5Pi over 4 ) + \text{cos}(5Pi over 6 + 5Pi over 4 ) \right]