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

Level 2

This math topic focuses on identifying trigonometric ratios—specifically tangent (tan), secant (sec), cosecant (csc), and cotangent (cot)—in relation to specific radians positions on the unit circle. Each problem presents an image of the unit circle with a highlighted section or angle, and asks to determine which trigonometric ratio corresponds to that highlighted element. The problems give two choices for answers, each expressed in radians, challenging understanding of trigonometric concepts within the framework of the unit circle. This is an integral part of learning trigonometry, particularly in visualizing and interpreting the relationships between angles and ratios.

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 Name (Radians) Worksheet

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Trigonemetry, Unit Circle Ratios (Tan, Sec, Csc, Cot) - To Ratio Name...
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{tan}(7Pi over 4 )
b A LaTex expression showing \text{cot}(7Pi over 4 )
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{csc}(2Pi over 3 )
b A LaTex expression showing \text{cot}(2Pi 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{tan}(4Pi over 3 )
b A LaTex expression showing \text{sec}(4Pi 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{cot}(5Pi over 4 )
b A LaTex expression showing \text{sec}(5Pi over 4 )
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{cot}(3Pi over 4 )
b A LaTex expression showing \text{tan}(3Pi over 4 )
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{cot}(2Pi over 3 )
b A LaTex expression showing \text{tan}(2Pi over 3 )
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{tan}(5Pi over 6 )
b A LaTex expression showing \text{sec}(5Pi over 6 )
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{cos}(3Pi over 4 )
b A LaTex expression showing \text{tan}(3Pi over 4 )