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Trigonometry Identities - Double Angle to Identity (Radians)

Level 1

This math topic focuses on practicing the manipulation and application of trigonometric identities, specifically double-angle identities in radians. The problems require completing trigonometric expressions based on given templates. Skills practiced include recognizing and transforming trigonometric formulas related to sine, cosine, and tangent functions using double angles. The problems vary in difficulty, employing trigonometric expressions at different angle measures such as \( \frac{\pi}{4} \), \( \frac{7\pi}{6} \), \( \frac{5\pi}{4} \), and \( \frac{5\pi}{3} \). This topic helps strengthen the understanding of fundamental trigonometric identities and their applications.

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

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Trigonometry Identities - Double Angle to Identity (Radians) Worksheet

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Trigonometry Identities - Double Angle to Identity (Radians)
1
A LaTex expression showing \text{tan}{(2 times Pi over 4 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{tan}(Pi over 4 )\text{cot}(Pi over 4 )
b A LaTex expression showing =\frac{2\text{tan}(Pi over 4 )}{1-\text{tan} to the power of 2 (Pi over 4 )}
2
A LaTex expression showing \text{tan}{(2 times 7Pi over 6 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{\text{tan}(7Pi over 6 )}{1-2\text{tan}(7Pi over 6 )}
b A LaTex expression showing =\frac{2\text{tan}(7Pi over 6 )}{1-\text{tan} to the power of 2 (7Pi over 6 )}
3
A LaTex expression showing \text{sin}{(2 times 7Pi over 4 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =\text{sin}(7Pi over 4 )\text{cos}(7Pi over 4 )
b A LaTex expression showing =\frac{2\text{tan}(7Pi over 4 )}{1+\text{tan} to the power of 2 (7Pi over 4 )}
4
A LaTex expression showing \text{tan}{(2 times 7Pi over 4 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{tan}(7Pi over 4 )\text{cot}(7Pi over 4 )
b A LaTex expression showing =\frac{2\text{tan}(7Pi over 4 )}{1-\text{tan} to the power of 2 (7Pi over 4 )}
5
A LaTex expression showing \text{cos}{(2 times Pi over 6 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =\text{cos} to the power of 2 (Pi over 6 ) + \text{sin} to the power of 2 (Pi over 6 )
b A LaTex expression showing =\frac{1-\text{tan} to the power of 2 (Pi over 6 )}{1+\text{tan} to the power of 2 (Pi over 6 )}
6
A LaTex expression showing \text{cos}{(2 times 5Pi over 4 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{cos} to the power of 2 (5Pi over 4 ) + 1
b A LaTex expression showing =1 - 2\text{sin} to the power of 2 (5Pi over 4 )
7
A LaTex expression showing \text{cos}{(2 times 5Pi over 3 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{\text{tan} to the power of 2 (5Pi over 3 ) - 1}{1+\text{tan} to the power of 2 (5Pi over 3 )}
b A LaTex expression showing =\text{cos} to the power of 2 (5Pi over 3 ) - \text{sin} to the power of 2 (5Pi over 3 )
8
A LaTex expression showing \text{tan}{(2 times 4Pi over 3 )}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{tan}(4Pi over 3 )\text{cot}(4Pi over 3 )
b A LaTex expression showing =\frac{2\text{tan}(4Pi over 3 )}{1-\text{tan} to the power of 2 (4Pi over 3 )}