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

Level 1

This math topic focuses on exploring the inverse relationships among trigonometric ratios in the context of the unit circle. It involves determining what inverse ratio corresponds to given trigonometric functions like secant (\text{sec}), cosecant (\text{csc}), tangent (\text{tan}), and cotangent (\text{cot}). Each question presents a trigonometric expression and asks the learner to identify the appropriate inverse ratio. This practice is intended to deepen understanding of trigonometric identities and relationships 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 (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}(\gamma)
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{sec}(\gamma) = 1 over \text{sin (\gamma)}
b A LaTex expression showing \text{sec}(\gamma) = 1 over \text{cos (\gamma)}
2
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{tan (\theta)}
b A LaTex expression showing \text{cot}(\theta) = 1 over \text{csc (\theta)}
3
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{sec (\alpha)}
b A LaTex expression showing \text{tan}(\alpha) = 1 over \text{cot (\alpha)}
4
A LaTex expression showing \text{sin}(\beta)
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{sin}(\beta) = 1 over \text{sec (\beta)}
b A LaTex expression showing \text{sin}(\beta) = 1 over \text{csc (\beta)}
5
A LaTex expression showing \text{cos}(\alpha)
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cos}(\alpha) = 1 over \text{sec (\alpha)}
b A LaTex expression showing \text{cos}(\alpha) = 1 over \text{csc (\alpha)}
6
A LaTex expression showing \text{cos}(\gamma)
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cos}(\gamma) = 1 over \text{sec (\gamma)}
b A LaTex expression showing \text{cos}(\gamma) = 1 over \text{csc (\gamma)}
7
A LaTex expression showing \text{cot}(\beta)
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{cot}(\beta) = 1 over \text{tan (\beta)}
b A LaTex expression showing \text{cot}(\beta) = 1 over \text{csc (\beta)}
8
A LaTex expression showing \text{tan}(\gamma)
What inverse ratio would give this trigonometry ratio?
a A LaTex expression showing \text{tan}(\gamma) = 1 over \text{sec (\gamma)}
b A LaTex expression showing \text{tan}(\gamma) = 1 over \text{cot (\gamma)}