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Trigonemetry, Unit Circle Ratios (Tan, Sec, Csc, Cot) - To Ratio As Inverse (Degrees)

Level 1

This math topic focuses on understanding and applying trigonometric ratios using the unit circle, specifically the tangent, secant, cosecant, and cotangent functions. The problems involve identifying the correct trigonometric ratio that corresponds to a given highlighted dimension on the unit circle, expressed as inverses in degree measure. Each question is presented with a visual representation of the unit circle and a couple of multiple-choice answers formatted in LaTeX expressions, challenging students to connect geometric visualizations with trigonometric identities and calculations.

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

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Trigonemetry, Unit Circle Ratios (Tan, Sec, Csc, Cot) - To Ratio As Inverse (Degrees) Worksheet

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Trigonemetry, Unit Circle Ratios (Tan, Sec, Csc, Cot) - To Ratio As I...
1
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{cos}(45 to the power of circle ) = 1 over \text{csc (45 to the power of circle )}
b A LaTex expression showing \text{cos}(45 to the power of circle ) = 1 over \text{sec (45 to the power of circle )}
2
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{cos}(30 to the power of circle ) = 1 over \text{csc (30 to the power of circle )}
b A LaTex expression showing \text{cos}(30 to the power of circle ) = 1 over \text{sec (30 to the power of circle )}
3
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{cos}(60 to the power of circle ) = 1 over \text{sec (60 to the power of circle )}
b A LaTex expression showing \text{sin}(60 to the power of circle ) = 1 over \text{csc (60 to the power of circle )}
4
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{cos}(60 to the power of circle ) = 1 over \text{sec (60 to the power of circle )}
b A LaTex expression showing \text{tan}(60 to the power of circle ) = 1 over \text{cot (60 to the power of circle )}
5
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{sec}(30 to the power of circle ) = 1 over \text{cos (30 to the power of circle )}
b A LaTex expression showing \text{sec}(30 to the power of circle ) = 1 over \text{sin (30 to the power of circle )}
6
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{sec}(60 to the power of circle ) = 1 over \text{cos (60 to the power of circle )}
b A LaTex expression showing \text{sec}(60 to the power of circle ) = 1 over \text{sin (60 to the power of circle )}
7
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{csc}(30 to the power of circle ) = 1 over \text{sin (30 to the power of circle )}
b A LaTex expression showing \text{sec}(30 to the power of circle ) = 1 over \text{cos (30 to the power of circle )}
8
An svg image showing a math problem
What trigonometry ratio gives the highlighted dimension on the unit circle?
a A LaTex expression showing \text{sec}(30 to the power of circle ) = 1 over \text{sin (30 to the power of circle )}
b A LaTex expression showing \text{sec}(30 to the power of circle ) = 1 over \text{cos (30 to the power of circle )}