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

Level 1

This topic focuses on practicing trigonometric identities, specifically testing the correctness of sum to product identities in various problems. Each question presents a trigonometric identity involving functions like sine or cosine, using variables expressed in radians. The task is to determine if the given identity is correct, with the question structure being a true/false format. The identities are formatted for review of applying formulas to solve or verify trigonometric equations. This helps in enhancing skills in recognizing and manipulating trigonometric identities, a fundamental aspect of higher-level mathematics especially in calculus and physics.

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

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

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

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(Pi over 6 )}-\text{sin}{(5Pi over 3 )} = 2 \text{sin}{( (\frac{Pi over 6 - 5Pi over 3 )}{2})} \text{cos}{( (\frac{Pi over 6 + 5Pi over 3 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(Pi over 3 )}-\text{sin}{(7Pi over 4 )} = 2 \text{sin}{( (\frac{Pi over 3 - 7Pi over 4 )}{2})} \text{cos}{( (\frac{Pi over 3 + 7Pi over 4 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(2Pi over 3 )}+\text{sin}{(Pi over 6 )} = 2 \text{sin}{( (\frac{2Pi over 3 + Pi over 6 )}{2})} \text{cos}{( (\frac{2Pi over 3 - Pi over 6 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(Pi over 3 )}+\text{sin}{(Pi over 6 )} = 2 \text{sin}{( (\frac{Pi over 3 + Pi over 6 )}{2})} \text{cos}{( (\frac{Pi over 3 - Pi over 6 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{cos}{(5Pi over 3 )}-\text{cos}{(11Pi over 6 )} = \text{cos}{( (\frac{5Pi over 3 + 11Pi over 6 )}{2})} \text{sin}{( (\frac{5Pi over 3 + 11Pi over 6 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(Pi over 6 )}+\text{sin}{(Pi over 4 )} = 2 \text{sin}{( (\frac{Pi over 6 + Pi over 4 )}{2})} \text{cos}{( (\frac{Pi over 6 - Pi over 4 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{cos}{(Pi over 3 )}+\text{cos}{(2Pi over 3 )} = 2 \text{cos}{( 2 over (\frac{Pi {3} + 2Pi over 3 )})} \text{cos}{( (\frac{Pi over 3 - 2Pi over 3 )}{2})}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(11Pi over 6 )}-\text{sin}{(5Pi over 4 )} = -2 \text{sin}{( 2 over (\frac{11Pi {6} )})} \text{cos}{( (\frac{11Pi over 6 - 5Pi over 4 )}{2})}$

Yes