Questions and Answers
What is the derivative of sin(x)?
cos(x)
What is the derivative of cos(x)?
-sin(x)
What is the derivative of tan(x)?
sec^2(x)
What is the derivative of csc(x)?
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What is the derivative of sec(x)?
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What is the derivative of cot(x)?
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What is sin^2(x) + cos^2(x)?
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What is tan^2(x) + 1?
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What is 1 + cot^2(x)?
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What is the reciprocal of csc(x)?
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What is the reciprocal of sec(x)?
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What is the reciprocal of cot(x)?
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What is the reciprocal of sin(x)?
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What is the reciprocal of cos(x)?
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What is the reciprocal of tan(x)?
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What is tan(x)?
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What is cot(x)?
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Study Notes
Derivatives of Trigonometric Functions
- Derivative of sin(x) is cos(x)
- Derivative of cos(x) is -sin(x)
- Derivative of tan(x) is sec²(x)
- Derivative of csc(x) is -csc(x)cot(x)
- Derivative of sec(x) is sec(x)tan(x)
- Derivative of cot(x) is -csc²(x)
Fundamental Trigonometric Identities
- sin²(x) + cos²(x) equals 1
- tan²(x) + 1 equals sec²(x)
- 1 + cot²(x) equals csc²(x)
Reciprocals of Trigonometric Functions
- Reciprocal of csc(x) is 1/sin(x)
- Reciprocal of sec(x) is 1/cos(x)
- Reciprocal of cot(x) is 1/tan(x)
- Reciprocal of sin(x) is 1/csc(x)
- Reciprocal of cos(x) is 1/sec(x)
- Reciprocal of tan(x) is 1/cot(x)
Definitions of Trigonometric Functions
- tan(x) is defined as sin(x)/cos(x)
- cot(x) is defined as cos(x)/sin(x)
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Description
This quiz covers the derivatives of fundamental trigonometric functions including sine, cosine, tangent, cosecant, secant, and cotangent. Perfect for students looking to reinforce their understanding of calculus concepts related to trigonometry.
