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Trigonometry, Negative Angles Identity (Equations) - Cos/Sin/Tan to Identity (Degrees)

Level 1

This math topic focuses on understanding the properties of trigonometric functions of negative angles within the context of trigonometric identities. It requires analyzing and identifying whether the sine, cosine, or tangent of a negative angle equals the positive angle's trigonometric value, or its negative counterpart. Problems involve basic identities such as \(\sin(-\theta) = -\sin(\theta)\), \(\cos(-\theta) = \cos(\theta)\), and \(\tan(-\theta) = -\tan(\theta)\). This subject is an introduction to further exploration of trigonometric identities.

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

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Trigonometry, Negative Angles Identity (Equations) - Cos/Sin/Tan to Identity (Degrees) Worksheet

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Trigonometry, Negative Angles Identity (Equations) - Cos/Sin/Tan to I...
1
What is true about the tangent of this negative angle?
A LaTex expression showing \text{tan}(-60 to the power of circle )
a A LaTex expression showing \text{tan}(-60 to the power of circle ) = -\text{tan}(60 to the power of circle )
b A LaTex expression showing \text{tan}(-60 to the power of circle ) = \text{tan}(60 to the power of circle )
2
What is true about the tangent of this negative angle?
A LaTex expression showing \text{tan}(-135 to the power of circle )
a A LaTex expression showing \text{tan}(-135 to the power of circle ) = -\text{tan}(135 to the power of circle )
b A LaTex expression showing \text{tan}(-135 to the power of circle ) = \text{tan}(135 to the power of circle )
3
What is true about the sine of this negative angle?
A LaTex expression showing \text{sin}(-30 to the power of circle )
a A LaTex expression showing \text{sin}(-30 to the power of circle ) = \text{sin}(30 to the power of circle )
b A LaTex expression showing \text{sin}(-30 to the power of circle ) = -\text{sin}(30 to the power of circle )
4
What is true about the tangent of this negative angle?
A LaTex expression showing \text{tan}(-45 to the power of circle )
a A LaTex expression showing \text{tan}(-45 to the power of circle ) = \text{tan}(45 to the power of circle )
b A LaTex expression showing \text{tan}(-45 to the power of circle ) = -\text{tan}(45 to the power of circle )
5
What is true about the cosine of this negative angle?
A LaTex expression showing \text{cos}(-30 to the power of circle )
a A LaTex expression showing \text{cos}(-30 to the power of circle ) = \text{cos}(30 to the power of circle )
b A LaTex expression showing \text{cos}(-30 to the power of circle ) = -\text{cos}(30 to the power of circle )
6
What is true about the tangent of this negative angle?
A LaTex expression showing \text{tan}(-120 to the power of circle )
a A LaTex expression showing \text{tan}(-120 to the power of circle ) = \text{tan}(120 to the power of circle )
b A LaTex expression showing \text{tan}(-120 to the power of circle ) = -\text{tan}(120 to the power of circle )
7
What is true about the cosine of this negative angle?
A LaTex expression showing \text{cos}(-150 to the power of circle )
a A LaTex expression showing \text{cos}(-150 to the power of circle ) = -\text{cos}(150 to the power of circle )
b A LaTex expression showing \text{cos}(-150 to the power of circle ) = \text{cos}(150 to the power of circle )
8
What is true about the cosine of this negative angle?
A LaTex expression showing \text{cos}(-120 to the power of circle )
a A LaTex expression showing \text{cos}(-120 to the power of circle ) = -\text{cos}(120 to the power of circle )
b A LaTex expression showing \text{cos}(-120 to the power of circle ) = \text{cos}(120 to the power of circle )