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Trigonometry Identities - Double Angle Identity True/False (Radians)

Level 1

This topic focuses on verifying the correctness of trigonometric double-angle identities presented in radians. Each problem presents a different trigonometric expression involving the sine, cosine, or tangent of double angles such as \( \frac{2\pi}{3}, \frac{5\pi}{4}, \) or \( \frac{7\pi}{4}\) and asks whether the given identity is correct. By choosing "Yes" or "No", students can practice understanding and applying double-angle identities in a true/false format. This is part of a broader introduction to trigonometric identities.

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

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Trigonometry Identities - Double Angle Identity True/False (Radians) Worksheet

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