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Trigonometry Identities - Sum/Difference to Identity (Radians)

Level 1

This math topic focuses on trigonometric identities, specifically how to convert sum and difference expressions into identities using radians. It includes problems where learners apply formulae of sine, cosine, and tangent for sum and difference to solve for the complete identity expressions. The problems entail both interpreting and filling in the correct trigonometric identities based on given expressions involving the addition or subtraction of angles measured in radians. This helps in enhancing skills in handling and simplifying trigonometric functions within mathematical and applied contexts.

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

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Trigonometry Identities - Sum/Difference to Identity (Radians) Worksheet

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Trigonometry Identities - Sum/Difference to Identity (Radians)
1
Complete the sum/difference identity for this expression
A LaTex expression showing \text{sin}{(3Pi over 4 - 7Pi over 4 )}
a A LaTex expression showing =\text{sin}{(3Pi over 4 )}\text{cos}{(7Pi over 4 )} - \text{cos}{(3Pi over 4 )}\text{sin}{(7Pi over 4 )}
b A LaTex expression showing =\text{sin}{(3Pi over 4 )}\text{cos}{(7Pi over 4 )} + \text{cos} to the power of 2 {(3Pi over 4 )}
2
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(4Pi over 3 + 5Pi over 4 )}
a A LaTex expression showing =\text{sin} to the power of 2 {(4Pi over 3 )} - \text{cos}{(4Pi over 3 )}\text{sin}{(5Pi over 4 )}
b A LaTex expression showing =\text{cos}{(4Pi over 3 )}\text{cos}{(5Pi over 4 )} - \text{sin}{(4Pi over 3 )}\text{sin}{(5Pi over 4 )}
3
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(5Pi over 4 + 4Pi over 3 )}
a A LaTex expression showing =\text{sin}{(5Pi over 4 )}\text{cos}{(4Pi over 3 )} + \text{cos}{(5Pi over 4 )}\text{sin}{(4Pi over 3 )}
b A LaTex expression showing =\text{cos}{(5Pi over 4 )}\text{cos}{(4Pi over 3 )} - \text{sin}{(5Pi over 4 )}\text{sin}{(4Pi over 3 )}
4
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(11Pi over 6 + 3Pi over 4 )}
a A LaTex expression showing =\text{sin}{(11Pi over 6 )}\text{sin}{(3Pi over 4 )} - \text{cos}{(11Pi over 6 )}\text{cos}{(3Pi over 4 )}
b A LaTex expression showing =\text{cos}{(11Pi over 6 )}\text{cos}{(3Pi over 4 )} - \text{sin}{(11Pi over 6 )}\text{sin}{(3Pi over 4 )}
5
Complete the sum/difference identity for this expression
A LaTex expression showing \text{sin}{(5Pi over 3 + Pi over 3 )}
a A LaTex expression showing =\text{sin}{(5Pi over 3 )}\text{cos}{(Pi over 3 )} + \text{cos}{(5Pi over 3 )}\text{sin}{(Pi over 3 )}
b A LaTex expression showing =\text{sin} to the power of 2 {(5Pi over 3 )} - \text{cos}{(5Pi over 3 )}\text{sin}{(Pi over 3 )}
6
Complete the sum/difference identity for this expression
A LaTex expression showing \text{sin}{(5Pi over 6 + Pi over 6 )}
a A LaTex expression showing =\text{sin}{(5Pi over 6 )}\text{cos}{(Pi over 6 )} - \text{cos}{(5Pi over 6 )}\text{sin}{(Pi over 6 )}
b A LaTex expression showing =\text{sin}{(5Pi over 6 )}\text{cos}{(Pi over 6 )} + \text{cos}{(5Pi over 6 )}\text{sin}{(Pi over 6 )}
7
A LaTex expression showing \text{tan}{(7Pi over 6 + 3Pi over 4 )}
Complete the sum/difference identity for this expression
a A LaTex expression showing =\frac{\text{tan}(7Pi over 6 ) + \text{tan}(3Pi over 4 )}{1-\text{tan}(7Pi over 6 )\text{tan}(3Pi over 4 ) }
b A LaTex expression showing =\frac{\text{cos}(7Pi over 6 ) + \text{sin}(3Pi over 4 )}{1-\text{tan}(7Pi over 6 )\text{tan}(3Pi over 4 ) }
8
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(3Pi over 4 - 11Pi over 6 )}
a A LaTex expression showing =\text{sin}{(3Pi over 4 )}\text{cos}{(11Pi over 6 )} + \text{cos} to the power of 2 {(3Pi over 4 )}
b A LaTex expression showing =\text{cos}{(3Pi over 4 )}\text{cos}{(11Pi over 6 )} + \text{sin}{(3Pi over 4 )}\text{sin}{(11Pi over 6 )}