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Trigonometry, Negative Angles Identity (Equations) - Csc/Sec/Cot to Identity (Degrees)

Level 1

This math topic practices understanding trigonometric identities, specifically focused on the properties of trigonometric functions of negative angles. Through multiple-choice questions, it examines how the secant, cosecant, and cotangent of negative angles relate to their respective positive angles. Each problem presents an equation and asks to identify the correct identity transformation, using examples like \(\sec(-\theta)\), \(\csc(-\theta)\), and \(\cot(-\theta)\) where \(\theta\) represents values in degrees. This topic serves as an introduction to 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) - Csc/Sec/Cot to Identity (Degrees) Worksheet

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Trigonometry, Negative Angles Identity (Equations) - Csc/Sec/Cot to I...
1
What is true about the secant of this negative angle?
A LaTex expression showing \text{sec}(-30 to the power of circle )
a A LaTex expression showing \text{sec}(-30 to the power of circle ) = \text{sec}(30 to the power of circle )
b A LaTex expression showing \text{sec}(-30 to the power of circle ) = -\text{sec}(30 to the power of circle )
2
What is true about the cosecant of this negative angle?
A LaTex expression showing \text{csc}(-150 to the power of circle )
a A LaTex expression showing \text{csc}(-150 to the power of circle ) = -\text{csc}(150 to the power of circle )
b A LaTex expression showing \text{csc}(-150 to the power of circle ) = \text{csc}(150 to the power of circle )
3
What is true about the cosecant of this negative angle?
A LaTex expression showing \text{csc}(-45 to the power of circle )
a A LaTex expression showing \text{csc}(-45 to the power of circle ) = -\text{csc}(45 to the power of circle )
b A LaTex expression showing \text{csc}(-45 to the power of circle ) = \text{csc}(45 to the power of circle )
4
What is true about the cotangent of this negative angle?
A LaTex expression showing \text{cot}(-120 to the power of circle )
a A LaTex expression showing \text{cot}(-120 to the power of circle ) = \text{cot}(120 to the power of circle )
b A LaTex expression showing \text{cot}(-120 to the power of circle ) = -\text{cot}(120 to the power of circle )
5
What is true about the cotangent of this negative angle?
A LaTex expression showing \text{cot}(-45 to the power of circle )
a A LaTex expression showing \text{cot}(-45 to the power of circle ) = \text{cot}(45 to the power of circle )
b A LaTex expression showing \text{cot}(-45 to the power of circle ) = -\text{cot}(45 to the power of circle )
6
What is true about the secant of this negative angle?
A LaTex expression showing \text{sec}(-120 to the power of circle )
a A LaTex expression showing \text{sec}(-120 to the power of circle ) = \text{sec}(120 to the power of circle )
b A LaTex expression showing \text{sec}(-120 to the power of circle ) = -\text{sec}(120 to the power of circle )
7
What is true about the cosecant of this negative angle?
A LaTex expression showing \text{csc}(-60 to the power of circle )
a A LaTex expression showing \text{csc}(-60 to the power of circle ) = \text{csc}(60 to the power of circle )
b A LaTex expression showing \text{csc}(-60 to the power of circle ) = -\text{csc}(60 to the power of circle )
8
What is true about the cotangent of this negative angle?
A LaTex expression showing \text{cot}(-135 to the power of circle )
a A LaTex expression showing \text{cot}(-135 to the power of circle ) = -\text{cot}(135 to the power of circle )
b A LaTex expression showing \text{cot}(-135 to the power of circle ) = \text{cot}(135 to the power of circle )