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

Level 2

This math topic focuses on practicing trigonometric ratios and their inverses within the unit circle, specifically targeting angles measured in degrees. It includes problems that require identifying the inverse trigonometric ratio of given trigonometric functions such as tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). Each problem is structured to help learners understand the relationship between a trigonometric function and its reciprocal, enhancing their grasp of fundamental trigonometric identities and their applications in different quadrants of 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) - 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}(240 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cot}(240 to the power of circle ) = 1 over \text{tan (240 to the power of circle )}
b A LaTex expression showing \text{cot}(240 to the power of circle ) = 1 over \text{csc (240 to the power of circle )}
2
A LaTex expression showing \text{csc}(330 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(330 to the power of circle ) = 1 over \text{cos (330 to the power of circle )}
b A LaTex expression showing \text{csc}(330 to the power of circle ) = 1 over \text{sin (330 to the power of circle )}
3
A LaTex expression showing \text{sin}(315 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{sin}(315 to the power of circle ) = 1 over \text{sec (315 to the power of circle )}
b A LaTex expression showing \text{sin}(315 to the power of circle ) = 1 over \text{csc (315 to the power of circle )}
4
A LaTex expression showing \text{cot}(330 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cot}(330 to the power of circle ) = 1 over \text{tan (330 to the power of circle )}
b A LaTex expression showing \text{cot}(330 to the power of circle ) = 1 over \text{csc (330 to the power of circle )}
5
A LaTex expression showing \text{csc}(150 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(150 to the power of circle ) = 1 over \text{cos (150 to the power of circle )}
b A LaTex expression showing \text{csc}(150 to the power of circle ) = 1 over \text{sin (150 to the power of circle )}
6
A LaTex expression showing \text{csc}(210 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(210 to the power of circle ) = 1 over \text{sin (210 to the power of circle )}
b A LaTex expression showing \text{csc}(210 to the power of circle ) = 1 over \text{cos (210 to the power of circle )}
7
A LaTex expression showing \text{tan}(315 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{tan}(315 to the power of circle ) = 1 over \text{sec (315 to the power of circle )}
b A LaTex expression showing \text{tan}(315 to the power of circle ) = 1 over \text{cot (315 to the power of circle )}
8
A LaTex expression showing \text{cos}(135 to the power of circle )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cos}(135 to the power of circle ) = 1 over \text{sec (135 to the power of circle )}
b A LaTex expression showing \text{cos}(135 to the power of circle ) = 1 over \text{csc (135 to the power of circle )}