Lowest value that can get the sin and the cos

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SUMMARY

The sine (sin) and cosine (cos) functions have defined maximum and minimum values of 1 and -1, respectively. These values are derived from their geometric interpretations in right-angled triangles and are confirmed by the Pythagorean theorem, which states that sin²(x) + cos²(x) = 1. Understanding these fundamental properties is essential for further exploration of trigonometric identities and their applications.

PREREQUISITES
  • Basic understanding of trigonometric functions
  • Familiarity with right-angled triangles
  • Knowledge of the Pythagorean theorem
  • Concept of maxima and minima in mathematics
NEXT STEPS
  • Study the unit circle and its relationship to sine and cosine functions
  • Explore trigonometric identities, particularly sin²(x) + cos²(x) = 1
  • Learn about the derivatives of sine and cosine functions to find critical points
  • Investigate applications of sine and cosine in real-world scenarios, such as wave functions
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Students of mathematics, educators teaching trigonometry, and anyone interested in the foundational concepts of trigonometric functions.

Hepic
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lowest value that can get the "sin" and the "cos"

Sorry for my stupid question,but I forgot them.
What is the biggest and the lowest value that can get the "sin" and the "cos"

Thanks!
 
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Sorry, but you should check wikipedia before posting such questions, they just show you are lazy.
 
1.If you think of right-angled triangles, how are "cos(x)" and "sin(x)" defined in terms of the sides?
2. How can you rewrite the Pythagorean theorem in terms of a cos and sin identity?
3. What would this imply that the maxima/minima of cos and sin ought to be?
 

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