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Trigonometry Identities - Double Angle to Identity (Degrees)

Level 1

This math topic focuses on practicing trigonometric identities, specifically double-angle identities, using degrees. The problems involve completing expressions for sine and tangent functions at specific angle degrees, applying double-angle formulas. Each question provides a trigonometric expression with a missing identity and offers multiple choice answers for students to select the correct transformation or identity application. The covered angles vary across the questions, demonstrating practical use of these trigonometric identities in different contexts.

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 (Degrees) Worksheet

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Trigonometry Identities - Double Angle to Identity (Degrees)
1
Complete the double-angle identity for this expression
A LaTex expression showing \text{tan}{(2 times 60 to the power of circle )}
a A LaTex expression showing =2\text{tan}(60 to the power of circle )\text{cot}(60 to the power of circle )
b A LaTex expression showing =\frac{2\text{tan}(60 to the power of circle )}{1-\text{tan} to the power of 2 (60 to the power of circle )}
2
Complete the double-angle identity for this expression
A LaTex expression showing \text{sin}{(2 times 330 to the power of circle )}
a A LaTex expression showing =2\text{sin}(330 to the power of circle )\text{cos}(330 to the power of circle )
b A LaTex expression showing =\frac{\text{sin}(330 to the power of circle )\text{cos}(330 to the power of circle )}{2}
3
Complete the double-angle identity for this expression
A LaTex expression showing \text{tan}{(2 times 30 to the power of circle )}
a A LaTex expression showing =2\text{tan}(30 to the power of circle )\text{cot}(30 to the power of circle )
b A LaTex expression showing =\frac{2\text{tan}(30 to the power of circle )}{1-\text{tan} to the power of 2 (30 to the power of circle )}
4
A LaTex expression showing \text{tan}{(2 times 225 to the power of circle )}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{2\text{tan}(225 to the power of circle )}{1-\text{tan} to the power of 2 (225 to the power of circle )}
b A LaTex expression showing =\frac{\text{sin}(225 to the power of circle )\text{cos}(225 to the power of circle )}{2}
5
Complete the double-angle identity for this expression
A LaTex expression showing \text{tan}{(2 times 300 to the power of circle )}
a A LaTex expression showing =\frac{2\text{tan}(300 to the power of circle )}{1-\text{tan} to the power of 2 (300 to the power of circle )}
b A LaTex expression showing =2\text{tan}(300 to the power of circle )\text{cot}(300 to the power of circle )
6
A LaTex expression showing \text{sin}{(2 times 150 to the power of circle )}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{\text{tan}(150 to the power of circle )}{1+2\text{tan}(150 to the power of circle )}
b A LaTex expression showing =\frac{2\text{tan}(150 to the power of circle )}{1+\text{tan} to the power of 2 (150 to the power of circle )}
7
Complete the double-angle identity for this expression
A LaTex expression showing \text{sin}{(2 times 225 to the power of circle )}
a A LaTex expression showing =2\text{sin}(225 to the power of circle )\text{cos}(225 to the power of circle )
b A LaTex expression showing =\frac{\text{sin}(225 to the power of circle )\text{cos}(225 to the power of circle )}{2}
8
Complete the double-angle identity for this expression
A LaTex expression showing \text{sin}{(2 times 300 to the power of circle )}
a A LaTex expression showing =\frac{\text{sin}(300 to the power of circle )\text{cos}(300 to the power of circle )}{2}
b A LaTex expression showing =2\text{sin}(300 to the power of circle )\text{cos}(300 to the power of circle )