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

Level 2

This math topic focuses on trigonometry, specifically exploring the unit circle ratios (Tangent, Secant, Cosecant, Cotangent). It emphasizes understanding the relationships and inverse relationships between these trigonometric ratios, using Greek letter notation to represent angles. Students practice finding inverse ratios of given trigonometric functions, enhancing their grasp of fundamental trigonometric identities and their applications within the unit circle context. This involves identifying correct expressions for the inverses of secant, tangent, and other trigonometric functions.

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 (Greek Letter) Worksheet

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