Reciprocal Identities in Trigonometry

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Questions and Answers

What is the reciprocal identity of $ an heta$?

  • $rac{1}{rac{1}{ an heta}}$
  • $rac{1}{ an^2 heta}$
  • $rac{1}{ an heta}$ (correct)
  • $rac{1}{ an^{-1} heta}$

For $ heta$, given that $rac{1}{ ext{Reciprocal of} an heta} = $

  • $rack heta^2}{1}$
  • $rac{1}{ heta}$
  • $ an heta$ (correct)
  • $ heta$

What is the $ ext{Reciprocal of} ext(csc} heta?

  • $ heta_{ heta}$
  • $tan^{-1} heta$
  • $rac{1}{ ext{Reciprocal of} heta}$ (correct)
  • $ g heta$

What is the reciprocal identity of $ heta$

<p>$sec heta$ (A)</p> Signup and view all the answers

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Study Notes

Reciprocal Identities

  • sin⁡θ\sin \thetasinθ is the reciprocal of csc⁡θ\csc \thetacscθ, meaning sin⁡θ=1csc⁡θ\sin \theta = \frac{1}{\csc \theta}sinθ=cscθ1​
  • csc⁡θ\csc \thetacscθ is the reciprocal of sin⁡θ\sin \thetasinθ, meaning csc⁡θ=1sin⁡θ\csc \theta = \frac{1}{\sin \theta}cscθ=sinθ1​
  • cos⁡θ\cos \thetacosθ is the reciprocal of sec⁡θ\sec \thetasecθ, meaning cos⁡θ=1sec⁡θ\cos \theta = \frac{1}{\sec \theta}cosθ=secθ1​
  • sec⁡θ\sec \thetasecθ is the reciprocal of cos⁡θ\cos \thetacosθ, meaning sec⁡θ=1cos⁡θ\sec \theta = \frac{1}{\cos \theta}secθ=cosθ1​
  • tan⁡θ\tan \thetatanθ is the reciprocal of cot⁡θ\cot \thetacotθ, meaning tan⁡θ=1cot⁡θ\tan \theta = \frac{1}{\cot \theta}tanθ=cotθ1​
  • cot⁡θ\cot \thetacotθ is the reciprocal of tan⁡θ\tan \thetatanθ, meaning cot⁡θ=1tan⁡θ\cot \theta = \frac{1}{\tan \theta}cotθ=tanθ1

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