Unraveling the Mystery of Theta: Solving Cot(2theta) = 2

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SUMMARY

The discussion focuses on solving the equation cot(2θ) = 2. Participants clarify that to solve this equation, one should take the reciprocal, leading to tan(2θ) = 0.5. This transformation allows for the use of a calculator to find the angle 2θ. The key takeaway is the application of trigonometric identities to simplify the problem, specifically the relationship between cotangent and tangent.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cotangent and tangent.
  • Familiarity with trigonometric identities, particularly cot(θ) = 1/tan(θ).
  • Basic algebra skills for manipulating equations.
  • Ability to use scientific calculators for trigonometric calculations.
NEXT STEPS
  • Learn how to use trigonometric identities to simplify complex equations.
  • Explore the properties of inverse trigonometric functions, particularly the tangent function.
  • Practice solving trigonometric equations using a scientific calculator.
  • Study the unit circle to better understand angle measures in trigonometry.
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and anyone looking to improve their skills in solving trigonometric equations.

mattmannmf
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what is Theta?

Cot (2theta) = 2

I have no idea how to get the answer. algebraically or in my calculator
 
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Well, you don't have the inverse cottangent button on your calculator, so you might want to turn that cotangent into something that has an inverse button on your calculator... how about tangent?
 
ok:

so cot (2 theta)= 2

can be:
(2 theta) = tan(2)

is that correct?
 
Not quite.

cot(\theta)=\frac{1}{tan(\theta)}
 
I have no idea than..
 
Try taking the reciprocal of both sides...

I'll do one step for you.

Original equation...

cot(2\theta)=2

Take the reciprocal...

\frac{1}{cot(2\theta)}=\frac{1}{2}

And use the identity I told you before...

tan(2\theta)=.5

And you can solve it from there with a good calculator!
 

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