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

Level 2

This math topic focuses on identifying and relating various trigonometric ratios in the context of the unit circle. Students are practiced on determining specific trigonometric ratios — tangent (tan), secant (sec), cosecant (csc), and cotangent (cot) — based on given angles in degrees. Additionally, problems include identifying the inverse relationships among these ratios, emphasizing a deep understanding of how each ratio relates to its counterpart and the unit circle. Overall, it provides an in-depth exploration of trigonometric concepts using visual depictions and calculations based on the unit circle.

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{sin}(150 to the power of circle ) = 1 over \text{csc (150 to the power of circle )}
b A LaTex expression showing \text{cos}(150 to the power of circle ) = 1 over \text{sec (150 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{tan}(330 to the power of circle ) = 1 over \text{cot (330 to the power of circle )}
b A LaTex expression showing \text{tan}(330 to the power of circle ) = 1 over \text{sec (330 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}(240 to the power of circle ) = 1 over \text{sec (240 to the power of circle )}
b A LaTex expression showing \text{sin}(240 to the power of circle ) = 1 over \text{csc (240 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{csc}(300 to the power of circle ) = 1 over \text{sin (300 to the power of circle )}
b A LaTex expression showing \text{sec}(300 to the power of circle ) = 1 over \text{cos (300 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{csc}(315 to the power of circle ) = 1 over \text{sin (315 to the power of circle )}
b A LaTex expression showing \text{sec}(315 to the power of circle ) = 1 over \text{cos (315 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{cot}(330 to the power of circle ) = 1 over \text{csc (330 to the power of circle )}
b A LaTex expression showing \text{cot}(330 to the power of circle ) = 1 over \text{tan (330 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{sin}(150 to the power of circle ) = 1 over \text{sec (150 to the power of circle )}
b A LaTex expression showing \text{sin}(150 to the power of circle ) = 1 over \text{csc (150 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{tan}(315 to the power of circle ) = 1 over \text{cot (315 to the power of circle )}
b A LaTex expression showing \text{cos}(315 to the power of circle ) = 1 over \text{sec (315 to the power of circle )}