Proof of Trigonometric Identities: Sin(-theta), Cos(-theta), Tan(-theta)

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SUMMARY

The discussion focuses on proving the trigonometric identities Sin(-theta) = -Sin(theta), Cos(-theta) = Cos(theta), and Tan(-theta) = -Tan(theta). The proof for sine and cosine can be easily visualized through their graphs, while an analytic approach involves understanding their periodicity. The relationship of tangent with sine and cosine further confirms the identity for tangent. Utilizing the unit circle and right-triangle values is essential for a comprehensive understanding of these identities.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Familiarity with the unit circle and right-triangle geometry
  • Knowledge of periodic functions in mathematics
  • Basic graphing skills for visualizing trigonometric functions
NEXT STEPS
  • Study the periodicity of trigonometric functions
  • Learn about the unit circle and its application in trigonometry
  • Explore graphical representations of sine, cosine, and tangent functions
  • Investigate the relationships between trigonometric identities
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone seeking to deepen their understanding of sine, cosine, and tangent functions.

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Homework Statement


Can some one please give me the proof or somewhere I can find the proof or just an explanation why

Sin(-theta) = -Sin(theta
Cos(-theta) = cos(theta)
Tan(-theta)= -Tan(theta)

Thank you..

Homework Equations





The Attempt at a Solution

 
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You can see the result for sine and cosine easily if you graph them. If you want a more analytic approach you can use the periodicy.

Once you figure out why it's true for sine and cosine, you can use the tangent's relationship with the sine and cosine to see why the third result is true.
 
Examine the Right-triangle values on the Unit Circle.
 

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