A Guide to Growing Your Own Herbs""Growing Herbs: A Beginner's Guide

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SUMMARY

This discussion focuses on the mathematical identity for cotangent, specifically the formula $\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}$. Participants calculate values using this identity, with $\alpha = \tan^{-1} \frac{1}{2}$ leading to results for DP and CP, both equating to 6 and 2 respectively. The conversation highlights the application of trigonometric identities in problem-solving.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with the cotangent function
  • Basic algebraic manipulation skills
  • Knowledge of inverse trigonometric functions
NEXT STEPS
  • Study advanced trigonometric identities
  • Learn applications of cotangent in calculus
  • Explore inverse trigonometric functions in depth
  • Practice solving trigonometric equations
USEFUL FOR

Mathematics students, educators, and anyone interested in enhancing their understanding of trigonometric functions and identities.

Albert1
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Albert said:
View attachment 2748

we have $\tan \alpha= \frac{1}{2} $
hence $\tan 2\alpha= \frac{2*\frac{1}{2}}{1-\frac{1}{4}}= \frac{4}{3} $

hence $DP = AD\tan\,2 \alpha =6$
so CP = 2
 
Albert said:
View attachment 2748

[sp]Remembering the trigonometric identity...

$\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}\ (1)$

... because is $\displaystyle \alpha = \tan^{-1} \frac{1}{2}$ You have...

$\displaystyle \text{DP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$[/sp]

Kind regards

$\chi$ $\sigma$
 
Last edited:
chisigma said:
[sp]Remembering the trigonometric identity...

$\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}\ (1)$

... because is $\displaystyle \alpha = \tan^{-1} \frac{1}{2}$ You have...

$\displaystyle \text{CP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$[/sp]

Kind regards

$\chi$ $\sigma$

DP = 6 hence CP = 2
 
thanks, kaliprasad and chisigma
you got it !
CP=2
 

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