Sin -270 different from sin - 90 exact and aprox values?

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SUMMARY

The exact value of sin(-270 degrees) is 1, derived from its reference angle of +90 degrees. The confusion arises from the negative angle, where the sine of the reference angle sin(90 degrees) equals 1. This discussion clarifies that reference angles are always considered positive, resolving the misunderstanding regarding the sine function's output for negative angles.

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  • Understanding of trigonometric functions, specifically sine.
  • Knowledge of reference angles in trigonometry.
  • Familiarity with angle measurement in degrees.
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  • Study the unit circle and its application in trigonometry.
  • Learn about the properties of sine and cosine functions for negative angles.
  • Explore the concept of reference angles in greater detail.
  • Practice solving trigonometric equations involving negative angles.
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Students studying trigonometry, educators teaching trigonometric concepts, and anyone seeking to clarify the behavior of sine functions with negative angles.

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Homework Statement



Homework related question:Write the exact value of sin(-270)

The Attempt at a Solution



I had this same question before but to write it in approximate value. for an aprox value i simply just plug it into my calculator and get: 1. Pretty exact for an approximate value. When i solve it the exact way. (No calculator) i determine that the Reference angle for -270 degrees is -90 degrees. then i sin -90 degrees and get -1. The answer is 1. I don't understand.
 
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Senjai said:

Homework Statement



Homework related question:Write the exact value of sin(-270)

The Attempt at a Solution



I had this same question before but to write it in approximate value. for an aprox value i simply just plug it into my calculator and get: 1. Pretty exact for an approximate value. When i solve it the exact way. (No calculator) i determine that the Reference angle for -270 degrees is -90 degrees. then i sin -90 degrees and get -1. The answer is 1. I don't understand.
The reference angle for -270 degrees is +90 degrees. sin(90 deg.) = 1, exactly.
 
Oh! Ref angles are always positive.. sorry.. Thanks for your time!
 

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