Pre-Calculus Identities Quiz

What is the reciprocal identity of sin(x)?

What is the reciprocal identity of cos(x)?

What is the reciprocal identity of csc(x)?

What is the reciprocal identity of sec(x)?

What is the reciprocal identity of tan(x)?

What is the quotient identity of tan(x)?

What is the quotient identity of cot(x)?

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

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

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 cos(2x)?

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

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))

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.