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?

1/sinθ Signup and view all the answers

What is the reciprocal identity of secθ?

1/cosθ Signup and view all the answers

What is the reciprocal identity of cotθ?

1/tanθ Signup and view all the answers

What is the quotient identity of tanθ?

sinθ/cosθ Signup and view all the answers

What is the quotient identity of cotθ?

cosθ/sinθ Signup and view all the answers

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

1 Signup and view all the answers

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

(sec^2)θ Signup and view all the answers

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

csc^2θ Signup and view all the answers

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

-sinθ Signup and view all the answers

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

cosθ Signup and view all the answers

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

-tanθ Signup and view all the answers

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

-cscθ Signup and view all the answers

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

secθ Signup and view all the answers

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

-cotθ Signup and view all the answers

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

cosθ Signup and view all the answers

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

sinθ Signup and view all the answers

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

secθ Signup and view all the answers

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

cscθ Signup and view all the answers

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

cotθ Signup and view all the answers

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

tanθ Signup and view all the answers

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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Description

Test your knowledge of trigonometric reciprocal identities with these flashcards. Each card presents an identity and its definition, helping you solidify your understanding of key concepts in trigonometry.