Equivalent Expression for Cot 50 Degrees

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Discussion Overview

The discussion revolves around finding an equivalent expression for cotangent of 50 degrees, exploring both degree and radian measures. Participants examine the relationships between cotangent and tangent functions.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks how to find the equivalent expression for cot 50 degrees and suggests that their calculation leads to tan 130 degrees, questioning their approach.
  • Another participant prefers to work in radians and provides a conversion of 50 degrees to radians, stating that cot(50 degrees) can be expressed as tan(40 degrees) using the identity cot(α) = tan(π/2 - α).
  • A later reply expresses understanding and appreciation for the clarification provided.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial approach to finding the equivalent expression, but there is agreement on the identity used to relate cotangent and tangent.

Contextual Notes

The discussion includes a conversion between degrees and radians, and the use of trigonometric identities, but does not resolve the initial confusion regarding the calculation leading to tan 130 degrees.

TonyC
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How do I go about finding the equivalent expression for cot 50 degrees?

When I work the problem, I come up with tan 130 degrees.

Where am I going wrong?
 
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I rather work in radians, if you don't mind.

[tex]50^\circ = \frac{{5\pi }}{{18}}[/tex]

We know that:
[tex]\cot \left( \alpha \right) = \tan \left( {\frac{\pi }{2} - \alpha } \right)[/tex]

So:
[tex]\cot \left( {\frac{{5\pi }}{{18}}} \right) = \tan \left( {\frac{\pi }{2} - \frac{{5\pi }}{{18}}} \right) = \tan \left( {\frac{{2\pi }}{9}} \right) = \tan \left( {40^\circ } \right)[/tex]
 
That makes perfect sense now...

The light has come on, thank you
 
No problem :smile:
 

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