Is sin(3.6) Negative in Quadrant III?

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Discussion Overview

The discussion centers around the value of sin(3.6) and whether it is negative, particularly focusing on the interpretation of the angle in radians versus degrees. The scope includes mathematical reasoning and clarification of trigonometric concepts.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested, Mathematical reasoning

Main Points Raised

  • Some participants question why sin(3.6) is considered negative, asserting that it should be positive between -90 and 90 degrees.
  • Others clarify that 3.6 is interpreted in radians, which changes the context of the sine function's value.
  • One participant notes that if x is between -90° and 0°, sin(x) is negative, suggesting a misunderstanding of the angle's measure.
  • A later reply states that since π < 3.6 < 3π/2, 3.6 radians lies in quadrant III where sine values are negative.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of the angle measure, with some asserting that 3.6 should be viewed in degrees while others maintain it is in radians. The discussion remains unresolved as differing viewpoints persist.

Contextual Notes

There is an underlying assumption regarding the interpretation of angle measures (degrees vs. radians) that is not explicitly addressed, leading to confusion about the sign of the sine value.

Chadi B Ghaith
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Why is sin(3.6) Negative? Why is sin(3.6) negative? It makes no sense. It should be positive between -90 and 90 degrees.
 
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It makes sense if 3.6 is in radian.
 
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Chadi B Ghaith said:
Why is sin(3.6) NEGATIVE? Why is sin(3.6) negative? It makes no sense. It should be positive between -90 and 90 degrees.
sin(3.6°) > -0, but 3.6 by itself is considered to be in radian measure.

Also,if x is between -90° and 0°, sin(x) is negative.
 
Mark44 said:
sin(3.6°) > -0, but 3.6 by itself is considered to be in radian measure.

Also,if x is between -90° and 0°, sin(x) is negative.

Thank you Mark44.
 
Because, π<3.6<3π/2 ... 3.6 radians lies in quadrant III where sine values are negative.
 

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