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

Level 1

This math topic focuses on mastering trigonometry within the framework of the unit circle, particularly dealing with trigonometric ratios such as tangent (tan), secant (sec), cosecant (csc), and cotangent (cot) when expressed in radians. Students are challenged to identify inverse relationships between these trigonometric functions, understanding for example how \(\tan(\theta)\) relates inversely with \(\cot(\theta)\) or how \(\csc(\theta)\) is the inverse of \(\sin(\theta)\). This practice explores these concepts through explicit problem-solving, enhancing students' understanding of fundamental trigonometric identities and their applications within 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 (Radians) Worksheet

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