Pre-Calculus Identities Quiz

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.