Secant Cosecant Calculator

Secant, cosecant, and cotangent are the reciprocal trigonometric functions. They are defined as the reciprocals of cosine, sine, and tangent respectively.

Definitions:

• Secant: sec θ = 1 / cos θ
• Cosecant: csc θ = 1 / sin θ
• Cotangent: cot θ = cos θ / sin θ = 1 / tan θ

Common Values:

Angle	sec	csc	cot
0°	1	Undefined	Undefined
30°	2/sqrt(3) = 1.1547	2	sqrt(3) = 1.7321
45°	sqrt(2) = 1.4142	sqrt(2) = 1.4142	1
60°	2	2/sqrt(3) = 1.1547	1/sqrt(3) = 0.5774
90°	Undefined	1	0

When Are They Undefined?

• sec θ is undefined when cos θ = 0 (at 90°, 270°, etc.)
• csc θ is undefined when sin θ = 0 (at 0°, 180°, 360°, etc.)
• cot θ is undefined when sin θ = 0 (same as csc)

Identities Involving Reciprocal Functions:

• 1 + tan²θ = sec²θ
• 1 + cot²θ = csc²θ
• sec²θ - tan²θ = 1

These identities appear frequently in calculus, especially when integrating trigonometric expressions.