Finding Exact Value of d tan (π/12)

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SUMMARY

The discussion focuses on calculating the exact value of d tan(π/12) using compound angle formulas. Participants emphasize the importance of understanding the definitions of "d" and the specific compound angle formulas involved. Key formulas mentioned include sin(π/6) = 2sin(π/12)cos(π/12) and tan(π/12) = sin(π/12)/cos(π/12). These formulas are essential for deriving the exact value of d tan(π/12).

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and tangent.
  • Familiarity with compound angle formulas in trigonometry.
  • Knowledge of radians and their conversion to degrees.
  • Basic algebra skills for manipulating trigonometric identities.
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  • Study the derivation and application of compound angle formulas in trigonometry.
  • Learn how to calculate exact values of trigonometric functions for common angles.
  • Explore the relationship between sine, cosine, and tangent functions.
  • Practice solving trigonometric equations involving angles in radians.
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Students studying trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric identities and angle calculations.

rachael
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Use the compound angle formulas and appropriate angles to find the exact value of each
of the following:
D. d tan (pi/12)

thank you
 
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rachael said:
Use the compound angle formulas and appropriate angles to find the exact value of each
of the following:
D. d tan (pi/12)

thank you

Alright, what have you done? In particular what are the "compound angle formulas" and what is "d"?
 
Hints:

1.\sin \frac{\pi}{6} = 2\sin \frac{\pi}{12} \cos \frac{\pi}{12}

2.\tan \frac{\pi}{12}=\frac{\sin\frac{\pi}{12}}{\cos\frac{\pi}{12}}

Daniel.
 

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