Questions and Answers
What is the reciprocal identity of sinθ?
What is the reciprocal identity of cosθ?
What is the reciprocal identity of tanθ?
What is the reciprocal identity of cscθ?
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What is the reciprocal identity of secθ?
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What is the reciprocal identity of cotθ?
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What is the quotient identity of tanθ?
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What is the quotient identity of cotθ?
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What does the Pythagorean identity (sin^2)θ + (cos^2)θ equal?
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What does the Pythagorean identity (tan^2)θ + 1 equal?
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What does the Pythagorean identity (cot^2)θ + 1 equal?
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What is the even and odd identity for sin(-θ)?
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What is the even and odd identity for cos(-θ)?
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What is the even and odd identity for tan(-θ)?
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What is the even and odd identity for csc(-θ)?
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What is the even and odd identity for sec(-θ)?
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What is the even and odd identity for cot(-θ)?
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What is the cofunction identity for sin((π/2) - θ)?
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What is the cofunction identity for cos((π/2) - θ)?
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What is the cofunction identity for csc((π/2) - θ)?
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What is the cofunction identity for sec((π/2) - θ)?
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What is the cofunction identity for tan((π/2) - θ)?
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What is the cofunction identity for cot((π/2) - θ)?
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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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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.
