Trigonometric-Identity Problem (Quick Question)

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SUMMARY

The discussion centers on a trigonometric identity problem involving quadrants in a coordinate system. Participants identify a potential typo regarding the placement of angle $B$ in either Quadrant I (QI) or Quadrant III (QIII). Despite the typo, it is concluded that the answers remain consistent regardless of the quadrant due to the nature of trigonometric functions. However, one participant raises a valid concern about the sign changes that occur when switching quadrants, which could affect the final answer.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with the unit circle and quadrants
  • Knowledge of angle properties in different quadrants
  • Basic algebra for manipulating trigonometric equations
NEXT STEPS
  • Study the implications of quadrant placement on trigonometric functions
  • Explore the unit circle and its significance in trigonometry
  • Learn about sign conventions for trigonometric functions in different quadrants
  • Review common trigonometric identities and their applications
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Students studying trigonometry, educators teaching trigonometric concepts, and anyone interested in understanding the nuances of trigonometric identities and their quadrant implications.

MIIF
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Shouldn't the quadrant in the orange circle (or whatever it looks like) match with the quadrant in the green one (i.e., Quadrant I)? Thanks.https://uploads.tapatalk-cdn.com/20180601/f3bb14bdcd0ee44fbf84ed81cf266d40.jpghttps://uploads.tapatalk-cdn.com/20180601/aa252ceb0ebb22a7848051a85b6a9a29.jpg
 
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Yes, it looks like a typo. However the answers are the same whether $B$ is in QI or QIII.
 
Olinguito said:
Yes, it looks like a typo. However the answers are the same whether $B$ is in QI or QIII.
Yes, perhaps that's the case, but wouldn't the answers be different considering the quadrant difference (e.g., the sign switch for the answer in (a))?https://uploads.tapatalk-cdn.com/20180601/a861c1250b3bd26b068231593e477c43.jpghttps://uploads.tapatalk-cdn.com/20180601/a09baa55d2efcec59dbda1570322f355.jpg
 

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