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Questions and Answers
Which identity represents $cos(A + B)$?
Which identity represents $cos(A + B)$?
What is the correct formula for $tan(A/2)$?
What is the correct formula for $tan(A/2)$?
Which formula is valid for $tan(A - B)$?
Which formula is valid for $tan(A - B)$?
What does $sin(2A)$ equal to?
What does $sin(2A)$ equal to?
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Which equation correctly represents $1 + cot^2(A)$?
Which equation correctly represents $1 + cot^2(A)$?
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What is the formula for $sin(A)cos(B)$?
What is the formula for $sin(A)cos(B)$?
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Study Notes
Trigonometric Identities
Pythagorean Identities
- sin^2(A) + cos^2(A) = 1
- tan^2(A) + 1 = sec^2(A)
- 1 + cot^2(A) = csc^2(A)
Sum and Difference Identities
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
- tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
- tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))
Double Angle Identities
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos^2(A) - sin^2(A)
- tan(2A) = 2tan(A) / (1 - tan^2(A))
Half Angle Identities
- sin(A/2) = ±√((1 - cos(A)) / 2)
- cos(A/2) = ±√((1 + cos(A)) / 2)
- tan(A/2) = ±√((1 - cos(A)) / (1 + cos(A)))
Product Identities
- sin(A)cos(B) = (1/2)[sin(A + B) + sin(A - B)]
- cos(A)sin(B) = (1/2)[sin(A + B) - sin(A - B)]
- cos(A)cos(B) = (1/2)[cos(A + B) + cos(A - B)]
- sin(A)sin(B) = (1/2)[cos(A - B) - cos(A + B)]
Co-Function Identities
- sin(A) = cos(π/2 - A)
- cos(A) = sin(π/2 - A)
- tan(A) = cot(π/2 - A)
- cot(A) = tan(π/2 - A)
- sec(A) = csc(π/2 - A)
- csc(A) = sec(π/2 - A)
Trigonometric Identities
Pythagorean Identities
- The sum of sin^2(A) and cos^2(A) is always 1
- The sum of tan^2(A) and 1 is equal to sec^2(A)
- 1 plus cot^2(A) is equal to csc^2(A)
Sum and Difference Identities
- The sine of the sum of two angles A and B is sin(A)cos(B) + cos(A)sin(B)
- The sine of the difference of two angles A and B is sin(A)cos(B) - cos(A)sin(B)
- The cosine of the sum of two angles A and B is cos(A)cos(B) - sin(A)sin(B)
- The cosine of the difference of two angles A and B is cos(A)cos(B) + sin(A)sin(B)
- The tangent of the sum of two angles A and B is (tan(A) + tan(B)) / (1 - tan(A)tan(B))
- The tangent of the difference of two angles A and B is (tan(A) - tan(B)) / (1 + tan(A)tan(B))
Double Angle Identities
- The sine of 2A is 2sin(A)cos(A)
- The cosine of 2A is cos^2(A) - sin^2(A)
- The tangent of 2A is 2tan(A) / (1 - tan^2(A))
Half Angle Identities
- The sine of A/2 is ±√((1 - cos(A)) / 2)
- The cosine of A/2 is ±√((1 + cos(A)) / 2)
- The tangent of A/2 is ±√((1 - cos(A)) / (1 + cos(A)))
Product Identities
- The product of sin(A) and cos(B) is (1/2)[sin(A + B) + sin(A - B)]
- The product of cos(A) and sin(B) is (1/2)[sin(A + B) - sin(A - B)]
- The product of cos(A) and cos(B) is (1/2)[cos(A + B) + cos(A - B)]
- The product of sin(A) and sin(B) is (1/2)[cos(A - B) - cos(A + B)]
Co-Function Identities
- The sine of A is equal to the cosine of π/2 - A
- The cosine of A is equal to the sine of π/2 - A
- The tangent of A is equal to the cotangent of π/2 - A
- The cotangent of A is equal to the tangent of π/2 - A
- The secant of A is equal to the cosecant of π/2 - A
- The cosecant of A is equal to the secant of π/2 - A
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Description
Test your knowledge of trigonometric identities, including Pythagorean, sum and difference, and double angle identities. Practice with these essential formulas for trigonometry problems.
