Pre-Calculus Identities Quiz

Questions and Answers

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)?

sec(x)

1/cos(x)

1/sec(x) (correct)

sin(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)?

1/cos(x) Signup and view all the answers

What is the reciprocal identity of tan(x)?

1/cot(x) Signup and view all the answers

What is the quotient identity of tan(x)?

sin(x)/cos(x) Signup and view all the answers

What is the quotient identity of cot(x)?

cos(x)/sin(x) Signup and view all the answers

What is the cofunction identity of sin(π/2-x)?

cos(x) Signup and view all the answers

What is the cofunction identity of cos(π/2-x)?

sin(x) Signup and view all the answers

What is the Pythagorean identity involving sin and cos?

1 + tan²x = sec²x Signup and view all the answers

What is the double angle formula for sin(2x)?

2sin(x)cos(x) Signup and view all the answers

What is the double angle formula for cos(2x)?

cos²(x) - sin²(x) or 1 - 2sin²(x) or 2cos²(x) - 1 Signup and view all the answers

What is the double angle formula for tan(2x)?

2tan(x)/(1 - tan²(x)) Signup and view all the answers

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(π/2 - x) = cos(x)
cos(π/2 - x) = sin(x)
tan(π/2 - x) = cot(x)
cot(π/2 - x) = tan(x)
sec(π/2 - x) = csc(x)
csc(π/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))

Description

Test your knowledge of reciprocal identities in trigonometry with this quiz. Each question focuses on the relationships between sine, cosine, cosecant, secant, tangent, and cotangent. Prepare to deepen your understanding of these essential pre-calculus concepts.