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Trigonometry Identities - Product to Sum to Identity (Degrees)

Level 1

This math topic focuses on practicing trigonometric identities, specifically converting products of sine and cosine functions into sum and difference identities using degrees. The exercises require completing product-to-sum identities for various trigonometric expressions, reinforcing understanding of the algebraic manipulation and transformation of trigonometric functions. Each problem presents an expression involving angles measured in degrees and asks to rewrite it in terms of sums or differences of different trigonometric functions, providing multiple-choice answers to select from. This helps strengthen the application of trigonometric identities in mathematical problems.

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 (Degrees) Worksheet

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Trigonometry Identities - Product to Sum to Identity (Degrees)
1
Complete the product to sum identity for this expression
A LaTex expression showing \text{sin}{(135 to the power of circle )}\text{cos}{(45 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(135 to the power of circle + 45 to the power of circle ) + \text{sin}(135 to the power of circle - 45 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(135 to the power of circle + 45 to the power of circle ) + \text{sin}(135 to the power of circle - 45 to the power of circle ) \right]
2
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(315 to the power of circle )}\text{cos}{(210 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(315 to the power of circle + 210 to the power of circle ) + \text{sin}(315 to the power of circle - 210 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(315 to the power of circle - 210 to the power of circle ) + \text{cos}(315 to the power of circle + 210 to the power of circle ) \right]
3
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(30 to the power of circle )}\text{sin}{(210 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(30 to the power of circle + 210 to the power of circle ) - \text{sin}(30 to the power of circle - 210 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(30 to the power of circle + 210 to the power of circle ) + \text{cos} to the power of 2 (30 to the power of circle + 210 to the power of circle ) \right]
4
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(225 to the power of circle )}\text{cos}{(135 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(225 to the power of circle - 135 to the power of circle ) + \text{cos}(225 to the power of circle + 135 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(225 to the power of circle + 135 to the power of circle ) + \text{sin}(225 to the power of circle - 135 to the power of circle ) \right]
5
Complete the product to sum identity for this expression
A LaTex expression showing \text{sin}{(150 to the power of circle )}\text{cos}{(30 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{sin}(150 to the power of circle + 30 to the power of circle ) + \text{sin}(150 to the power of circle - 30 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(150 to the power of circle + 30 to the power of circle ) + \text{sin}(150 to the power of circle - 30 to the power of circle ) \right]
6
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(225 to the power of circle )}\text{cos}{(150 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(225 to the power of circle - 150 to the power of circle ) + \text{cos}(225 to the power of circle + 150 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(225 to the power of circle + 150 to the power of circle ) + \text{cos} to the power of 2 (225 to the power of circle + 150 to the power of circle ) \right]
7
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(135 to the power of circle )}\text{sin}{(30 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(135 to the power of circle + 30 to the power of circle ) + \text{cos} to the power of 2 (135 to the power of circle + 30 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{sin}(135 to the power of circle + 30 to the power of circle ) - \text{sin}(135 to the power of circle - 30 to the power of circle ) \right]
8
Complete the product to sum identity for this expression
A LaTex expression showing \text{cos}{(300 to the power of circle )}\text{cos}{(60 to the power of circle )}
a A LaTex expression showing =1 over 2 \left[ \text{cos}(300 to the power of circle - 60 to the power of circle ) + \text{cos}(300 to the power of circle + 60 to the power of circle ) \right]
b A LaTex expression showing =1 over 2 \left[ \text{cos}(300 to the power of circle + 60 to the power of circle ) + \text{cos} to the power of 2 (300 to the power of circle + 60 to the power of circle ) \right]