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

Level 1

This math topic focuses on practicing trigonometric identities, specifically the product-to-sum identities in radians. The problems require verifying whether given identities are correct. Each problem presents an identity and asks the learner to determine its validity using a true/false format. This involves critical thinking and a deep understanding of trigonometry concepts to correctly transform product expressions into sum or difference forms, enabling students to recognize and apply these identities in various mathematical scenarios.

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

Worksheet ViewUnit

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

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

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(4Pi over 3 )}\text{sin}{(2Pi over 3 )} = 1 over 2 \left[ \text{sin}(4Pi over 3 + 2Pi over 3 ) - \text{sin}(4Pi over 3 - 2Pi over 3 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(2Pi over 3 )}\text{cos}{(7Pi over 4 )} = 1 over 2 \left[ \text{sin}(2Pi over 3 + 7Pi over 4 ) + \text{sin}(2Pi over 3 - 7Pi over 4 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{sin}{(Pi over 4 )}\text{sin}{(3Pi over 4 )} = 1 over 2 \left[ \text{sin}(Pi over 4 + 3Pi over 4 ) + \text{sin}(Pi over 4 - 3Pi over 4 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{sin}{(2Pi over 3 )}\text{cos}{(11Pi over 6 )} = 1 over 2 \left[ \text{sin}(2Pi over 3 + 11Pi over 6 ) + \text{sin}(2Pi over 3 - 11Pi over 6 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{sin}{(5Pi over 6 )}\text{sin}{(7Pi over 4 )} = 1 over 2 \left[ \text{cos}(5Pi over 6 + 7Pi over 4 ) + \text{sin}(5Pi over 6 + 7Pi over 4 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(Pi over 3 )}\text{cos}{(7Pi over 6 )} = 1 over 2 \left[ \text{cos}(Pi over 3 + 7Pi over 6 ) + \text{cos} to the power of 2 (Pi over 3 + 7Pi over 6 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(5Pi over 4 )}\text{sin}{(5Pi over 3 )} = 1 over 2 \left[ \text{sin}(5Pi over 4 + 5Pi over 3 ) - \text{sin}(5Pi over 4 - 5Pi over 3 ) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{sin}{(Pi over 6 )}\text{sin}{(Pi over 3 )} = 1 over 2 \left[ \text{cos}(Pi over 6 + Pi over 3 ) + \text{sin}(Pi over 6 + Pi over 3 ) \right]$

Yes