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

Level 2

This topic focuses on trigonometric ratios associated with the unit circle, specifically tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). It involves identifying these ratios and their reciprocal relationships using inverse functions represented by Greek letters (such as alpha, beta, gamma, theta). Problems include matching dimensions on the unit circle with the corresponding trigonometric ratio. Each question includes images of the unit circle highlighting specific dimensions and possible answers showing the reciprocal relationship between trigonometric functions and their respective inverses.

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 (Greek Letter) 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{sin}(\alpha) = 1 over \text{csc (\alpha)}
b A LaTex expression showing \text{cos}(\alpha) = 1 over \text{sec (\alpha)}
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}(\alpha) = 1 over \text{sin (\alpha)}
b A LaTex expression showing \text{sec}(\alpha) = 1 over \text{cos (\alpha)}
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{sin}(\gamma) = 1 over \text{csc (\gamma)}
b A LaTex expression showing \text{cot}(\gamma) = 1 over \text{tan (\gamma)}
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{sin}(\theta) = 1 over \text{csc (\theta)}
b A LaTex expression showing \text{sin}(\theta) = 1 over \text{sec (\theta)}
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}(\beta) = 1 over \text{sec (\beta)}
b A LaTex expression showing \text{cos}(\beta) = 1 over \text{csc (\beta)}
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}(\gamma) = 1 over \text{cos (\gamma)}
b A LaTex expression showing \text{csc}(\gamma) = 1 over \text{sin (\gamma)}
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{cos}(\theta) = 1 over \text{sec (\theta)}
b A LaTex expression showing \text{tan}(\theta) = 1 over \text{cot (\theta)}
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}(\beta) = 1 over \text{sec (\beta)}
b A LaTex expression showing \text{sin}(\beta) = 1 over \text{csc (\beta)}