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Trigonometry Identities - Product to Sum Identity True/False (Degrees)

Level 1

This topic focuses on verifying trigonometric identities involving the product-to-sum formulas. Students are given true/false questions to determine the correctness of transformations of products of sine and cosine functions into their sum or difference equivalents. Each problem requires an understanding of trigonometry identities and their application in degrees. The task tests the ability to analyze and simplify expressions through specific identity validations.

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

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Trigonometry Identities - Product to Sum Identity True/False (Degrees) Worksheet

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Trigonometry Identities - Product to Sum Identity True/False (Degrees)
1
Is this product to sum identity correct?
A LaTex expression showing \text{sin}{(120 to the power of circle )}\text{sin}{(45 to the power of circle )} = 1 over 2 \left[ \text{sin}(120 to the power of circle + 45 to the power of circle ) + \text{sin}(120 to the power of circle - 45 to the power of circle ) \right]
a
Yes
b
No
2
Is this product to sum identity correct?
A LaTex expression showing \text{sin}{(30 to the power of circle )}\text{sin}{(45 to the power of circle )} = 1 over 2 \left[ \text{cos}(30 to the power of circle - 45 to the power of circle ) - \text{cos}(30 to the power of circle + 45 to the power of circle ) \right]
a
Yes
b
No
3
Is this product to sum identity correct?
A LaTex expression showing \text{cos}{(315 to the power of circle )}\text{cos}{(225 to the power of circle )} = 1 over 2 \left[ \text{cos}(315 to the power of circle - 225 to the power of circle ) + \text{cos}(315 to the power of circle + 225 to the power of circle ) \right]
a
Yes
b
No
4
Is this product to sum identity correct?
A LaTex expression showing \text{sin}{(225 to the power of circle )}\text{cos}{(150 to the power of circle )} = 1 over 2 \left[ \text{sin}(225 to the power of circle + 150 to the power of circle ) + \text{sin}(225 to the power of circle - 150 to the power of circle ) \right]
a
Yes
b
No
5
Is this product to sum identity correct?
A LaTex expression showing \text{sin}{(315 to the power of circle )}\text{sin}{(45 to the power of circle )} = 1 over 2 \left[ \text{cos}(315 to the power of circle - 45 to the power of circle ) - \text{cos}(315 to the power of circle + 45 to the power of circle ) \right]
a
Yes
b
No
6
Is this product to sum identity correct?
A LaTex expression showing \text{cos}{(225 to the power of circle )}\text{cos}{(60 to the power of circle )} = 1 over 2 \left[ \text{cos}(225 to the power of circle - 60 to the power of circle ) + \text{cos}(225 to the power of circle + 60 to the power of circle ) \right]
a
Yes
b
No
7
Is this product to sum identity correct?
A LaTex expression showing \text{cos}{(315 to the power of circle )}\text{cos}{(330 to the power of circle )} = 1 over 2 \left[ \text{sin}(315 to the power of circle + 330 to the power of circle ) + \text{sin}(315 to the power of circle - 330 to the power of circle ) \right]
a
Yes
b
No
8
Is this product to sum identity correct?
A LaTex expression showing \text{cos}{(45 to the power of circle )}\text{sin}{(120 to the power of circle )} = 1 over 2 \left[ \text{sin}(45 to the power of circle + 120 to the power of circle ) - \text{sin}(45 to the power of circle - 120 to the power of circle ) \right]
a
Yes
b
No