Basic Trig Identities + Important Formulas

Covers trig identities (reciprocal, quotient, Pythagorean, even & odd, and cofunction identities), sum and difference formulas, and double angle formulas.

Reciprocal: cosθ =

1/secθ

Reciprocal: sinθ =

1/cscθ

Reciprocal: tanθ =

1/cotθ

Reciprocal: secθ =

1/cosθ

Reciprocal: cscθ =

1/sinθ

Reciprocal: cotθ =

1/tanθ

Quotient: tanθ =

sinθ/cosθ

Quotient: cotθ =

cosθ/sinθ

Pythagorean: sin²θ + cos²θ =

1

Pythagorean: tan²θ + 1 =

sec²θ

Pythagorean: 1 + cot²θ =

csc²θ

Even & Odd: cos(-x) =

cosx

Even & Odd: sin(-x) =

-sinx

Even & Odd: tan(-x) =

-tanx

Even & Odd: sec(-x) =

secx

Even & Odd: csc(-x) =

-cscx

Even & Odd: cot(-x) =

-cotx

Cofunction: cos(π/2 - x) =

sinx

Cofunction: sin(π/2 - x) =

cosx

Cofunction: tan(π/2 - x) =

cotx

Cofunction: sec(π/2 - x) =

cscx

Cofunction: csc(π/2 - x) =

secx

Cofunction: cot(π/2 - x) =

tanx

Sum and Difference: sin(α + β) =

sin(α)cos(β) + cos(α)sin(β)

Sum and Difference: sin(α - β) =

sin(α)cos(β) - cos(α)sin(β)

Sum and Difference: cos(α + β) =

cos(α)cos(β) - sin(α)sin(β)

Sum and Difference: cos(α - β) =

cos(α)cos(β) + sin(α)sin(β)

Sum and Difference: tan(α + β) =

tan(α) + tan(β) / 1 - tan(α)tan(β)

Sum and Difference: tan(α - β) =

tan(α) - tan(β) / 1 + tan(α)tan(β)

Double Angle: sin(2α) =

2sin(α)cos(α)

Double Angle: cos(2α) =

cos²(α) - sin²(α)

or 2cos²(α) - 1

or 1 - 2sin²(α)

Double Angle: tan(2α) =

2tan(α) / 1 - tan²(α)