1=?
sin²θ + cos²θ
A Pythagorean Identity
sec²θ=?
1 + tan²θ
A Pythagorean Identity
csc²θ=
1 + cot²θ
What is a Pythagorean Identity?
Identities derived from the equation of the unit circle.
What is a reciprocal identity?
Identities which define the reciprocal functions in terms of sine and cosine.
csc θ =?
1 / sin θ
A reciprocal identity.
sec θ = ?
1 / cos θ
A reciprocal Identity
cot θ = ?
1 / tan θ = cos θ / sin θ
A reciprocal identity.
What is a quotient identity?
Identities derived from the reciprocal identities.
tan θ = ?
sin θ / cos θ
A quotient identity.
cot θ = ?
cos θ / sin θ
A quotient identity.
sin 2θ = ?
2 sin θ cos θ
cos 2θ = ?
cos²θ - sin²θ = 2 cos²θ - 1 = 1 - 2 sin²θ
tan 2θ = ?
(2 tan θ) / (1 - tan²θ)
sin²θ = ?
(1 - cos 2θ) / 2
cos²θ = ?
(1 + cos 2θ) / 2
tan²θ =
(1 - cos 2θ) / (1 + cos 2θ)
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)
