Trigonometry, Unit Circle Negative Angles Identity - Cos/Sin to Identity (Radians)

Level 1

This math topic explores trigonometric identities involving the cosine and sine of negative angles. The questions require understanding the symmetry properties of the unit circle, specifically how the cosine and sine functions behave when dealing with negative angles, expressed in radians. Each problem presents an angle, asking if the trigonometric function (cosine or sine) of the negative of that angle equals the function of the angle itself or its negative. This set of problems helps reinforce students' grasp of fundamental trigonometric identities and enhances their skills in working with the unit circle and radians within the context of trigonometry.

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

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Trigonometry, Unit Circle Negative Angles Identity - Cos/Sin to Identity (Radians) Worksheet

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Trigonometry, Unit Circle Negative Angles Identity - Cos/Sin to Ident...
1
An svg image showing a math problem
What is true about the cosine of this negative angle?
a A LaTex expression showing \text{cos}(-5Pi over 6 ) = -\text{cos}(5Pi over 6 )
b A LaTex expression showing \text{cos}(-5Pi over 6 ) = \text{cos}(5Pi over 6 )
2
An svg image showing a math problem
What is true about the cosine of this negative angle?
a A LaTex expression showing \text{cos}(-Pi over 6 ) = \text{cos}(Pi over 6 )
b A LaTex expression showing \text{cos}(-Pi over 6 ) = -\text{cos}(Pi over 6 )
3
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-3Pi over 4 ) = \text{sin}(3Pi over 4 )
b A LaTex expression showing \text{sin}(-3Pi over 4 ) = -\text{sin}(3Pi over 4 )
4
An svg image showing a math problem
What is true about the cosine of this negative angle?
a A LaTex expression showing \text{cos}(-2Pi over 3 ) = \text{cos}(2Pi over 3 )
b A LaTex expression showing \text{cos}(-2Pi over 3 ) = -\text{cos}(2Pi over 3 )
5
An svg image showing a math problem
What is true about the cosine of this negative angle?
a A LaTex expression showing \text{cos}(-3Pi over 4 ) = \text{cos}(3Pi over 4 )
b A LaTex expression showing \text{cos}(-3Pi over 4 ) = -\text{cos}(3Pi over 4 )
6
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-5Pi over 6 ) = \text{sin}(5Pi over 6 )
b A LaTex expression showing \text{sin}(-5Pi over 6 ) = -\text{sin}(5Pi over 6 )
7
An svg image showing a math problem
What is true about the cosine of this negative angle?
a A LaTex expression showing \text{cos}(-Pi over 4 ) = \text{cos}(Pi over 4 )
b A LaTex expression showing \text{cos}(-Pi over 4 ) = -\text{cos}(Pi over 4 )
8
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-Pi over 6 ) = -\text{sin}(Pi over 6 )
b A LaTex expression showing \text{sin}(-Pi over 6 ) = \text{sin}(Pi over 6 )