Trigonometry Identities - Power Reducing Identity True/False (Radians)

Level 1

This math topic covers trigonometric identities, specifically focusing on evaluating the correctness of power-reducing identities. The problems involve determining whether given expressions in radians, such as \(\cos^2(\frac{5\pi}{3}) = \frac{1+\cos(\frac{10\pi}{3})}{2}\) or \(\tan^2(\frac{4\pi}{3}) = \frac{1-\cos(\frac{8\pi}{3})}{1+\cos(\frac{8\pi}{3})}\), accurately represent power-reducing formulas. Each question provides a trigonometric identity and asks if it is correct, offering a choice of "Yes" or "No" for answers. This practice helps deepen understanding of trigonometric identities used to simplify powers of sine, cosine, and tangent functions.

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

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Trigonometry Identities - Power Reducing Identity True/False (Radians) Worksheet

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Trigonometry Identities - Power Reducing Identity True/False (Radians)
1
Is this power reducing identity correct?
A LaTex expression showing \text{cos} to the power of 2 {(5Pi over 3 )} = \frac{1+\text{cos}(2 times 5Pi over 3 )}{2}
a
Yes
b
No
2
Is this power reducing identity correct?
A LaTex expression showing \text{tan} to the power of 2 {(5Pi over 4 )} = \frac{1+\text{cos}(2 times 5Pi over 4 )}{2}
a
Yes
b
No
3
A LaTex expression showing \text{cos} to the power of 2 {(11Pi over 6 )} = 2 over 1+\text{cos (11Pi over 6 )}
Is this power reducing identity correct?
a
Yes
b
No
4
A LaTex expression showing \text{cos} to the power of 2 {(3Pi over 4 )} = \frac{1+\text{cos}(2 times 3Pi over 4 )}{1-\text{cos}(3Pi over 4 )}
Is this power reducing identity correct?
a
Yes
b
No
5
A LaTex expression showing \text{sin} to the power of 2 {(5Pi over 4 )} = \frac{1-\text{cos}(2 times 5Pi over 4 )}{2}
Is this power reducing identity correct?
a
Yes
b
No
6
A LaTex expression showing \text{tan} to the power of 2 {(4Pi over 3 )} = \frac{1-\text{cos}(2 times 4Pi over 3 )}{1+\text{cos}(2 times 4Pi over 3 )}
Is this power reducing identity correct?
a
Yes
b
No
7
A LaTex expression showing \text{cos} to the power of 2 {(Pi over 4 )} = \frac{1+\text{cos}(2 times Pi over 4 )}{2}
Is this power reducing identity correct?
a
Yes
b
No
8
A LaTex expression showing \text{cos} to the power of 2 {(5Pi over 3 )} = 2 over 1+\text{cos (5Pi over 3 )}
Is this power reducing identity correct?
a
Yes
b
No