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Trigonometry Identities - Power Reducing to Identity (Radians)

Level 1

This math topic focuses on practicing trigonometric identity transformations involving power reducing identities in radian measure. The problems require applying these trigonometric identities to express squared trigonometric functions, like sine and cosine squared, in different forms using double angle identities and related formulas. It's a beginner-level introduction, part of a broader unit aimed at mastering trigonometric identities. Each question presents a trigonometric expression with suggestions for its equivalent identity, pushing learners to choose or derive the correct transformation based on trigonometric properties.

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

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Trigonometry Identities - Power Reducing to Identity (Radians) Worksheet

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