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

Level 1

This topic covers basic trigonometric identities involving negative angles in the unit circle, primarily focusing on the properties of sine and cosine functions. The problems explore how these trigonometric functions behave when applied to negative angles, helping to understand whether each function, sine or cosine, returns the same value or the negative of the value when the angle sign is switched (i.e., θ to -θ). Such exercises are vital for mastering the concepts of symmetry in trigonometric functions as they relate to the unit circle.

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 (Greek Letter) 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}(-\theta) = -\text{cos}(\theta)
b A LaTex expression showing \text{cos}(-\theta) = \text{cos}(\theta)
2
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-\theta) = -\text{sin}(\theta)
b A LaTex expression showing \text{sin}(-\theta) = \text{sin}(\theta)
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}(-\gamma) = \text{sin}(\gamma)
b A LaTex expression showing \text{sin}(-\gamma) = -\text{sin}(\gamma)
4
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-\theta) = \text{sin}(\theta)
b A LaTex expression showing \text{sin}(-\theta) = -\text{sin}(\theta)
5
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-\beta) = -\text{sin}(\beta)
b A LaTex expression showing \text{sin}(-\beta) = \text{sin}(\beta)
6
An svg image showing a math problem
What is true about the cosine of this negative angle?
a A LaTex expression showing \text{cos}(-\beta) = \text{cos}(\beta)
b A LaTex expression showing \text{cos}(-\beta) = -\text{cos}(\beta)
7
An svg image showing a math problem
What is true about the sine of this negative angle?
a A LaTex expression showing \text{sin}(-\alpha) = -\text{sin}(\alpha)
b A LaTex expression showing \text{sin}(-\alpha) = \text{sin}(\alpha)
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}(-\gamma) = \text{sin}(\gamma)
b A LaTex expression showing \text{sin}(-\gamma) = -\text{sin}(\gamma)