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Questions and Answers
What is the reciprocal identity of sin(x)?
What is the reciprocal identity of sin(x)?
- 1/csc(x) (correct)
- csc(x)
- tan(x)
- sec(x)
What is the reciprocal identity of cos(x)?
What is the reciprocal identity of cos(x)?
- sec(x)
- 1/cos(x)
- 1/sec(x) (correct)
- sin(x)
What is the reciprocal identity of csc(x)?
What is the reciprocal identity of csc(x)?
- tan(x)
- sin(x)
- 1/sin(x) (correct)
- cot(x)
What is the reciprocal identity of sec(x)?
What is the reciprocal identity of sec(x)?
What is the reciprocal identity of tan(x)?
What is the reciprocal identity of tan(x)?
What is the quotient identity of tan(x)?
What is the quotient identity of tan(x)?
What is the quotient identity of cot(x)?
What is the quotient identity of cot(x)?
What is the cofunction identity of sin(Ï€/2-x)?
What is the cofunction identity of sin(Ï€/2-x)?
What is the cofunction identity of cos(Ï€/2-x)?
What is the cofunction identity of cos(Ï€/2-x)?
What is the Pythagorean identity involving sin and cos?
What is the Pythagorean identity involving sin and cos?
What is the double angle formula for sin(2x)?
What is the double angle formula for sin(2x)?
What is the double angle formula for cos(2x)?
What is the double angle formula for cos(2x)?
What is the double angle formula for tan(2x)?
What is the double angle formula for tan(2x)?
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Study Notes
Reciprocal Identities
- sin(x) = 1/csc(x)
- cos(x) = 1/sec(x)
- csc(x) = 1/sin(x)
- sec(x) = 1/cos(x)
- tan(x) = 1/cot(x)
- cot(x) = 1/tan(x)
Quotient Identities
- tan(x) = sin(x)/cos(x)
- cot(x) = cos(x)/sin(x)
Cofunction Identities
- sin(Ï€/2 - x) = cos(x)
- cos(Ï€/2 - x) = sin(x)
- tan(Ï€/2 - x) = cot(x)
- cot(Ï€/2 - x) = tan(x)
- sec(Ï€/2 - x) = csc(x)
- csc(Ï€/2 - x) = sec(x)
Pythagorean Identities
- sin²(x) + cos²(x) = 1
- 1 - cos²(x) = sin²(x)
- 1 - sin²(x) = cos²(x)
- sec²(x) - tan²(x) = 1
- 1 + tan²(x) = sec²(x)
- sec²(x) - 1 = tan²(x)
- csc²(x) - cot²(x) = 1
- 1 + cot²(x) = csc²(x)
- csc²(x) - 1 = cot²(x)
Even/Odd Identities
- sin(-x) = -sin(x) (Odd function)
- cos(-x) = cos(x) (Even function)
- tan(-x) = -tan(x) (Odd function)
- cot(-x) = -cot(x) (Odd function)
- sec(-x) = sec(x) (Even function)
- csc(-x) = -csc(x) (Odd function)
Sum and Difference Formulas
- sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β)
- cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β)
- tan(α ± β) = (tan(α) ± tan(β)) / (1 ∓ tan(α)tan(β))
Double Angle Formulas
- sin(2x) = 2sin(x)cos(x)
- cos(2x) = cos²(x) - sin²(x) = 1 - 2sin²(x) = 2cos²(x) - 1
- tan(2x) = 2tan(x) / (1 - tan²(x))
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