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

Level 1

This math topic focuses on identifying trigonometry ratios from illustrations of the unit circle, particularly involving the tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). These problems are presented in the context of radians, with questions asking to determine which trigonometric ratio corresponds to highlighted segments or angles in the unit circle diagrams. Students are expected to understand and compute reciprocal relationships like sec(θ) = 1/cos(θ), addressing fundamental trigonometric functions 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) - To Ratio As Inverse (Radians) 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{csc}(Pi over 3 ) = 1 over \text{sin (Pi over 3 )}
b A LaTex expression showing \text{sec}(Pi over 3 ) = 1 over \text{cos (Pi over 3 )}
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{sin}(Pi over 3 ) = 1 over \text{csc (Pi over 3 )}
b A LaTex expression showing \text{cos}(Pi over 3 ) = 1 over \text{sec (Pi over 3 )}
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{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 )}
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{cos}(Pi over 6 ) = 1 over \text{csc (Pi over 6 )}
b A LaTex expression showing \text{cos}(Pi over 6 ) = 1 over \text{sec (Pi over 6 )}
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{cos}(Pi over 3 ) = 1 over \text{csc (Pi over 3 )}
b A LaTex expression showing \text{cos}(Pi over 3 ) = 1 over \text{sec (Pi over 3 )}
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{sec}(Pi over 6 ) = 1 over \text{sin (Pi over 6 )}
b A LaTex expression showing \text{sec}(Pi over 6 ) = 1 over \text{cos (Pi over 6 )}
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{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 )}
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{sec}(Pi over 4 ) = 1 over \text{sin (Pi over 4 )}
b A LaTex expression showing \text{sec}(Pi over 4 ) = 1 over \text{cos (Pi over 4 )}