Fundamental Trig identities
Posted: February 1st, 2011, 7:20 pmPythagorean Identities
sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
1 + cot²θ = csc²θ
Reciprocal Identities
sin θ = 1 ⁄ csc θ
cos θ = 1 ⁄ sec θ
tan θ = 1 ⁄ cot θ
csc θ = 1 ⁄ sin θ
sec θ = 1 ⁄ cos θ
cot θ = 1 ⁄ tan θ
Quotient Identities
tan θ = sin θ ⁄ cos θ
cot θ = cos θ ⁄ sin θ
Even/Odd Identities
sin(−θ) = −sin θ
cos(−θ) = cos θ
tan(−θ) = −tan θ
csc(−θ) = −csc θ
sec(−θ) = sec θ
cot(−θ) = −cot θ
sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
1 + cot²θ = csc²θ
Reciprocal Identities
sin θ = 1 ⁄ csc θ
cos θ = 1 ⁄ sec θ
tan θ = 1 ⁄ cot θ
csc θ = 1 ⁄ sin θ
sec θ = 1 ⁄ cos θ
cot θ = 1 ⁄ tan θ
Quotient Identities
tan θ = sin θ ⁄ cos θ
cot θ = cos θ ⁄ sin θ
Even/Odd Identities
sin(−θ) = −sin θ
cos(−θ) = cos θ
tan(−θ) = −tan θ
csc(−θ) = −csc θ
sec(−θ) = sec θ
cot(−θ) = −cot θ