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Trigonometry Identities - Power Reducing to Identity (Degrees)

Level 1

This topic covers the application and manipulation of trigonometric identities, specifically focusing on power-reducing identities for sine, cosine, and tangent functions measured in degrees. Students are tasked with transforming expressions involving trigonometric functions raised to a power into equivalent forms using identities. The problems provided offer multiple-choice answers, requiring students to select the correct power-reducing identity transformations for given trigonometric expressions at various angles. This helps enhance understanding of trigonometry basics and prepares learners to solve complex trigonometric equations efficiently.

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 (Degrees) Worksheet

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Trigonometry Identities - Power Reducing to Identity (Degrees)
1
A LaTex expression showing \text{tan} to the power of 2 {(45 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =\frac{1-\text{cos}(2 times 45 to the power of circle )}{1+\text{cos}(2 times 45 to the power of circle )}
b A LaTex expression showing =2 over 1+\text{cos (45 to the power of circle )}
2
A LaTex expression showing \text{sin} to the power of 2 {(135 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =\frac{1-\text{cos}(2 times 135 to the power of circle )}{2}
b A LaTex expression showing =\frac{1-\text{cos}(2 times 135 to the power of circle )}{1+\text{cos}(135 to the power of circle )}
3
A LaTex expression showing \text{sin} to the power of 2 {(30 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =\frac{1+\text{cos}(2 times 30 to the power of circle )}{1-\text{cos}(30 to the power of circle )}
b A LaTex expression showing =\frac{1-\text{cos}(2 times 30 to the power of circle )}{2}
4
A LaTex expression showing \text{cos} to the power of 2 {(30 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =\frac{1+\text{cos}(2 times 30 to the power of circle )}{2}
b A LaTex expression showing =\frac{1+\text{cos}(2 times 30 to the power of circle )}{1-\text{cos}(30 to the power of circle )}
5
A LaTex expression showing \text{cos} to the power of 2 {(300 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =\frac{1+\text{cos}(2 times 300 to the power of circle )}{1-\text{cos}(300 to the power of circle )}
b A LaTex expression showing =\frac{1+\text{cos}(2 times 300 to the power of circle )}{2}
6
A LaTex expression showing \text{tan} to the power of 2 {(60 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =2 over 1+\text{cos (60 to the power of circle )}
b A LaTex expression showing =\frac{1-\text{cos}(2 times 60 to the power of circle )}{1+\text{cos}(2 times 60 to the power of circle )}
7
A LaTex expression showing \text{tan} to the power of 2 {(315 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =2 over 1+\text{cos (315 to the power of circle )}
b A LaTex expression showing =\frac{1-\text{cos}(2 times 315 to the power of circle )}{1+\text{cos}(2 times 315 to the power of circle )}
8
A LaTex expression showing \text{cos} to the power of 2 {(225 to the power of circle )}
Complete the power reducing identity for this expression
a A LaTex expression showing =\frac{1+\text{cos}(2 times 225 to the power of circle )}{1-\text{cos}(225 to the power of circle )}
b A LaTex expression showing =\frac{1+\text{cos}(2 times 225 to the power of circle )}{2}