Trigonometric Identities Practice

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Questions and Answers

What is the reciprocal identity of sinθ?

  • cosθ/sinθ
  • 1/sinθ
  • sinθ/cosθ
  • 1/cscθ (correct)

What is the reciprocal identity of cosθ?

  • secθ/cosθ
  • 1/secθ (correct)
  • cosθ/sinθ
  • 1/cosθ

What is the reciprocal identity of tanθ?

  • tanθ/secθ
  • sinθ/cosθ
  • 1/tanθ
  • 1/cotθ (correct)

What is the reciprocal identity of cscθ?

<p>1/sinθ (D)</p> Signup and view all the answers

What is the reciprocal identity of secθ?

<p>1/cosθ (D)</p> Signup and view all the answers

What is the reciprocal identity of cotθ?

<p>1/tanθ (A)</p> Signup and view all the answers

What is the quotient identity of tanθ?

<p>sinθ/cosθ (D)</p> Signup and view all the answers

What is the quotient identity of cotθ?

<p>cosθ/sinθ (B)</p> Signup and view all the answers

What does the Pythagorean identity (sin^2)θ + (cos^2)θ equal?

<p>1 (B)</p> Signup and view all the answers

What does the Pythagorean identity (tan^2)θ + 1 equal?

<p>(sec^2)θ (A)</p> Signup and view all the answers

What does the Pythagorean identity (cot^2)θ + 1 equal?

<p>csc^2θ (D)</p> Signup and view all the answers

What is the even and odd identity for sin(-θ)?

<p>-sinθ (D)</p> Signup and view all the answers

What is the even and odd identity for cos(-θ)?

<p>cosθ (B)</p> Signup and view all the answers

What is the even and odd identity for tan(-θ)?

<p>-tanθ (D)</p> Signup and view all the answers

What is the even and odd identity for csc(-θ)?

<p>-cscθ (A)</p> Signup and view all the answers

What is the even and odd identity for sec(-θ)?

<p>secθ (B)</p> Signup and view all the answers

What is the even and odd identity for cot(-θ)?

<p>-cotθ (B)</p> Signup and view all the answers

What is the cofunction identity for sin((π/2) - θ)?

<p>cosθ (B)</p> Signup and view all the answers

What is the cofunction identity for cos((π/2) - θ)?

<p>sinθ (A)</p> Signup and view all the answers

What is the cofunction identity for csc((π/2) - θ)?

<p>secθ (B)</p> Signup and view all the answers

What is the cofunction identity for sec((π/2) - θ)?

<p>cscθ (D)</p> Signup and view all the answers

What is the cofunction identity for tan((π/2) - θ)?

<p>cotθ (A)</p> Signup and view all the answers

What is the cofunction identity for cot((π/2) - θ)?

<p>tanθ (B)</p> Signup and view all the answers

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Study Notes

Reciprocal Identities

  • ( \sin \theta = \frac{1}{\csc \theta} )
  • ( \cos \theta = \frac{1}{\sec \theta} )
  • ( \tan \theta = \frac{1}{\cot \theta} )
  • ( \csc \theta = \frac{1}{\sin \theta} )
  • ( \sec \theta = \frac{1}{\cos \theta} )
  • ( \cot \theta = \frac{1}{\tan \theta} )

Quotient Identities

  • ( \tan \theta = \frac{\sin \theta}{\cos \theta} )
  • ( \cot \theta = \frac{\cos \theta}{\sin \theta} )

Pythagorean Identities

  • ( \sin^2 \theta + \cos^2 \theta = 1 )
  • ( \tan^2 \theta + 1 = \sec^2 \theta )
  • ( \cot^2 \theta + 1 = \csc^2 \theta )

Even and Odd Identities

  • ( \sin(-\theta) = -\sin \theta ) (odd)
  • ( \cos(-\theta) = \cos \theta ) (even)
  • ( \tan(-\theta) = -\tan \theta ) (odd)
  • ( \csc(-\theta) = -\csc \theta ) (odd)
  • ( \sec(-\theta) = \sec \theta ) (even)
  • ( \cot(-\theta) = -\cot \theta ) (odd)

Cofunction Identities

  • ( \sin\left(\frac{\pi}{2} - \theta\right) = \cos \theta )
  • ( \cos\left(\frac{\pi}{2} - \theta\right) = \sin \theta )
  • ( \csc\left(\frac{\pi}{2} - \theta\right) = \sec \theta )
  • ( \sec\left(\frac{\pi}{2} - \theta\right) = \csc \theta )
  • ( \tan\left(\frac{\pi}{2} - \theta\right) = \cot \theta )
  • ( \cot\left(\frac{\pi}{2} - \theta\right) = \tan \theta )

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