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

Level 2

This math topic focuses on trigonometry, specifically unit circle ratios including tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). The exercises specifically deal with finding inverse trigonometric ratios in radians. Each question presents a trigonometric expression and asks for the corresponding inverse ratio. It deepens understanding of the relationships between trigonometric functions and their reciprocals within the unit circle, leveraging radians as the unit for angle measures.

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 (Radians) Worksheet

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Trigonemetry, Unit Circle Ratios (Tan, Sec, Csc, Cot) - Ratio To Rati...
1
A LaTex expression showing \text{csc}(7Pi over 4 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(7Pi over 4 ) = 1 over \text{cos (7Pi over 4 )}
b A LaTex expression showing \text{csc}(7Pi over 4 ) = 1 over \text{sin (7Pi over 4 )}
2
A LaTex expression showing \text{csc}(3Pi over 4 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{csc}(3Pi over 4 ) = 1 over \text{sin (3Pi over 4 )}
b A LaTex expression showing \text{csc}(3Pi over 4 ) = 1 over \text{cos (3Pi over 4 )}
3
A LaTex expression showing \text{tan}(4Pi over 3 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{tan}(4Pi over 3 ) = 1 over \text{sec (4Pi over 3 )}
b A LaTex expression showing \text{tan}(4Pi over 3 ) = 1 over \text{cot (4Pi over 3 )}
4
A LaTex expression showing \text{sin}(5Pi over 3 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{sin}(5Pi over 3 ) = 1 over \text{csc (5Pi over 3 )}
b A LaTex expression showing \text{sin}(5Pi over 3 ) = 1 over \text{sec (5Pi over 3 )}
5
A LaTex expression showing \text{cot}(5Pi over 4 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cot}(5Pi over 4 ) = 1 over \text{csc (5Pi over 4 )}
b A LaTex expression showing \text{cot}(5Pi over 4 ) = 1 over \text{tan (5Pi over 4 )}
6
A LaTex expression showing \text{sin}(7Pi over 6 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{sin}(7Pi over 6 ) = 1 over \text{sec (7Pi over 6 )}
b A LaTex expression showing \text{sin}(7Pi over 6 ) = 1 over \text{csc (7Pi over 6 )}
7
A LaTex expression showing \text{cos}(5Pi over 4 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cos}(5Pi over 4 ) = 1 over \text{csc (5Pi over 4 )}
b A LaTex expression showing \text{cos}(5Pi over 4 ) = 1 over \text{sec (5Pi over 4 )}
8
A LaTex expression showing \text{cos}(2Pi over 3 )
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cos}(2Pi over 3 ) = 1 over \text{sec (2Pi over 3 )}
b A LaTex expression showing \text{cos}(2Pi over 3 ) = 1 over \text{csc (2Pi over 3 )}