Sinx and cosx in the second quadrant

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SUMMARY

The discussion centers on the trigonometric functions sine and cosine, specifically in relation to their values in the second quadrant of the unit circle. It is established that when sin(x) > 0 and cos(x) < 0, the angle x must indeed be located in the second quadrant. This is due to the fact that in this quadrant, the y-coordinates (sine values) are positive while the x-coordinates (cosine values) are negative, confirming the relationship between the signs of these functions and their respective quadrants.

PREREQUISITES
  • Understanding of the unit circle and its quadrants
  • Knowledge of trigonometric functions: sine and cosine
  • Familiarity with the properties of angles in different quadrants
  • Basic trigonometric identities and their applications
NEXT STEPS
  • Study the properties of angles in the unit circle
  • Learn about the relationship between trigonometric functions and their signs in different quadrants
  • Explore trigonometric identities and their proofs
  • Practice solving trigonometric equations involving sine and cosine
USEFUL FOR

This discussion is beneficial for students of trigonometry, mathematics educators, and anyone seeking to deepen their understanding of the unit circle and the behavior of trigonometric functions in various quadrants.

tmt1
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In a question we have sinx > 0 and cosx < 0.

The book says that from this we can determine that angle x is in the second quadrant. I am not understanding this leap.
 
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Think of the unit circle...in which quadrant do points on the circle have negative $x$-coordinates and positive $y$-coordinates?
 

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