Trig Ratio Values Using Bow-Tie Diagram: sin 45, cos 60, tan 30, tan 45

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SUMMARY

The discussion focuses on calculating specific trigonometric ratios using a "bow-tie" diagram. The values provided are: sin 45° = 1 / √2, cos 60° = 1 / 2, tan 30° = 1 / √3, and tan 45° = 1. The bow-tie diagram is mentioned as a tool to visualize related acute angles, although its relevance to the calculation of these ratios is questioned. The consensus confirms that the answers given are indeed correct and represent the fundamental nature of trigonometric functions as ratios.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine, cosine, tangent)
  • Familiarity with angle measurement in degrees
  • Knowledge of the bow-tie diagram for visualizing angle relationships
  • Ability to simplify square roots in mathematical expressions
NEXT STEPS
  • Study the derivation of trigonometric ratios for common angles (30°, 45°, 60°)
  • Explore the application of the bow-tie diagram in trigonometry
  • Learn about the unit circle and its relation to trigonometric functions
  • Investigate the properties of trigonometric identities and their proofs
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Students of mathematics, educators teaching trigonometry, and anyone seeking to deepen their understanding of trigonometric functions and their visual representations.

Imperil
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Use the "bow-tie" diagram to state the value of each trigonometric ratio.
a) sin 45
b) cos 60
c) tan 30
d) tan 45

My Answer:

a) 1 / \sqrt{2}
b) 1 / 2
c) 1 / \sqrt{3}
d) 1

Once again with this text the wording has thrown me off. It asks for the ratios but throws in that you should use the "bow-tie" diagram. All the diagram shows is that related acute angles of each quadrant, I don't see how that has any relation to this question.
 
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Your answers are correct. And they are ratios! Every trig function is a ratio.
 

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