Home
Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Grade 9Grade 10Grade 11Grade 12Math Themes
Explorers (Grades 1-3)Explorers Elite (1-3)Navigators (Grades 4-6)Navigators Elite (4-6)Challengers (Grades 7-9)Challengers Elite (7-9)Scholars (Grades 10-12)Scholars Elite (10-12)Schedule an Evaluation
Mobius MethodFlexible ClassesCompanySupport
Pricing
Ctrl+k
Sign InJoin

Trigonometry Identities - Sum to Product to Identity (Radians)

Level 1

This topic focuses on practicing trigonometric identities, specifically transitioning from sum to product identities (and vice versa) using radian measures. It involves solving and simplifying expressions using sine and cosine functions. Each problem presents an expression involving trigonometric sums or differences, for which the student must derive the equivalent product or sum identity. It targets foundational skills in manipulating and understanding relationships within trigonometric functions, essential for higher-level math and applications in physics and engineering.

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

more
WorksheetView

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

Mobius Math Academy logo
Trigonometry Identities - Sum to Product to Identity (Radians)
1
Complete the sum to product identity for this expression
A LaTex expression showing \text{sin}{(7Pi over 6 )}+\text{sin}{(Pi over 3 )}
a A LaTex expression showing =2 \text{sin}{( (\frac{7Pi over 6 + Pi over 3 )}{2})} \text{cos}{( (\frac{7Pi over 6 - Pi over 3 )}{2})}
b A LaTex expression showing =2 \text{cos}{( (\frac{7Pi over 6 - Pi over 3 )}{2})} - \text{sin}{( (\frac{7Pi over 6 + Pi over 3 )}{2})}
2
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(2Pi over 3 )}+\text{cos}{(7Pi over 6 )}
a A LaTex expression showing =2 \text{cos}{( (\frac{2Pi over 3 + 7Pi over 6 )}{2})} \text{cos}{( (\frac{2Pi over 3 - 7Pi over 6 )}{2})}
b A LaTex expression showing =2 \text{sin}{( (\frac{2Pi over 3 + 7Pi over 6 )}{2})} \text{sin}{( (\frac{2Pi over 3 - 7Pi over 6 )}{2})}
3
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(5Pi over 4 )}-\text{cos}{(2Pi over 3 )}
a A LaTex expression showing =-2 \text{sin}{( (\frac{5Pi over 4 + 2Pi over 3 )}{2})} \text{sin}{( (\frac{5Pi over 4 - 2Pi over 3 )}{2})}
b A LaTex expression showing =\text{cos}{( (\frac{5Pi over 4 + 2Pi over 3 )}{2})} \text{sin}{( (\frac{5Pi over 4 + 2Pi over 3 )}{2})}
4
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(2Pi over 3 )}+\text{cos}{(5Pi over 6 )}
a A LaTex expression showing =2 \text{sin}{( (\frac{2Pi over 3 + 5Pi over 6 )}{2})} \text{sin}{( (\frac{2Pi over 3 - 5Pi over 6 )}{2})}
b A LaTex expression showing =2 \text{cos}{( (\frac{2Pi over 3 + 5Pi over 6 )}{2})} \text{cos}{( (\frac{2Pi over 3 - 5Pi over 6 )}{2})}
5
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(5Pi over 4 )}+\text{cos}{(5Pi over 3 )}
a A LaTex expression showing =2 \text{sin}{( (\frac{5Pi over 4 + 5Pi over 3 )}{2})} \text{sin}{( (\frac{5Pi over 4 - 5Pi over 3 )}{2})}
b A LaTex expression showing =2 \text{cos}{( (\frac{5Pi over 4 + 5Pi over 3 )}{2})} \text{cos}{( (\frac{5Pi over 4 - 5Pi over 3 )}{2})}
6
Complete the sum to product identity for this expression
A LaTex expression showing \text{sin}{(5Pi over 4 )}+\text{sin}{(Pi over 6 )}
a A LaTex expression showing =2 \text{sin}{( (\frac{5Pi over 4 + Pi over 6 )}{2})} \text{cos}{( (\frac{5Pi over 4 - Pi over 6 )}{2})}
b A LaTex expression showing =2 \text{cos}{( (\frac{5Pi over 4 - Pi over 6 )}{2})} - \text{sin}{( (\frac{5Pi over 4 + Pi over 6 )}{2})}
7
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(2Pi over 3 )}-\text{cos}{(Pi over 6 )}
a A LaTex expression showing =\text{cos}{( (\frac{2Pi over 3 + Pi over 6 )}{2})} \text{sin}{( (\frac{2Pi over 3 + Pi over 6 )}{2})}
b A LaTex expression showing =-2 \text{sin}{( (\frac{2Pi over 3 + Pi over 6 )}{2})} \text{sin}{( (\frac{2Pi over 3 - Pi over 6 )}{2})}
8
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(Pi over 4 )}+\text{cos}{(3Pi over 4 )}
a A LaTex expression showing =2 \text{cos}{( (\frac{Pi over 4 + 3Pi over 4 )}{2})} \text{cos}{( (\frac{Pi over 4 - 3Pi over 4 )}{2})}
b A LaTex expression showing =\text{cos}{( (\frac{Pi over 4 + 3Pi over 4 )}{2})} \text{cos}{( (\frac{Pi over 4 + 3Pi over 4 )}{2})}