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

Level 1

This math topic covers trigonometry and unit circle ratios, focusing on recognizing trigonometric ratios (Tan, Sec, Csc, Cot) and their inverse relationships in degrees. Students engaged with these problems will determine inverse ratios corresponding to given trigonometric expressions, helping to deepen their understanding of trigonometric identities and properties within the unit circle, as part of broader practice in trigonometry.

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) - Ratio To Ratio As Inverse (Degrees) Worksheet

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Trigonemetry, Unit Circle Ratios (Tan, Sec, Csc, Cot) - Ratio To Rati...
1
A LaTex expression showing \text{cot}(60 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cot}(60 to the power of circle ) = 1 over \text{tan (60 to the power of circle )}
b A LaTex expression showing \text{cot}(60 to the power of circle ) = 1 over \text{csc (60 to the power of circle )}
2
A LaTex expression showing \text{cot}(30 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cot}(30 to the power of circle ) = 1 over \text{tan (30 to the power of circle )}
b A LaTex expression showing \text{cot}(30 to the power of circle ) = 1 over \text{csc (30 to the power of circle )}
3
A LaTex expression showing \text{csc}(60 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(60 to the power of circle ) = 1 over \text{sin (60 to the power of circle )}
b A LaTex expression showing \text{csc}(60 to the power of circle ) = 1 over \text{cos (60 to the power of circle )}
4
A LaTex expression showing \text{tan}(60 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{tan}(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
A LaTex expression showing \text{cos}(30 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cos}(30 to the power of circle ) = 1 over \text{sec (30 to the power of circle )}
b A LaTex expression showing \text{cos}(30 to the power of circle ) = 1 over \text{csc (30 to the power of circle )}
6
A LaTex expression showing \text{tan}(45 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{tan}(45 to the power of circle ) = 1 over \text{sec (45 to the power of circle )}
b A LaTex expression showing \text{tan}(45 to the power of circle ) = 1 over \text{cot (45 to the power of circle )}
7
A LaTex expression showing \text{csc}(30 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(30 to the power of circle ) = 1 over \text{cos (30 to the power of circle )}
b A LaTex expression showing \text{csc}(30 to the power of circle ) = 1 over \text{sin (30 to the power of circle )}
8
A LaTex expression showing \text{sin}(45 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{sin}(45 to the power of circle ) = 1 over \text{csc (45 to the power of circle )}
b A LaTex expression showing \text{sin}(45 to the power of circle ) = 1 over \text{sec (45 to the power of circle )}