Secant (sec) - Trigonometry function

In a right triangle, the secant of an angle is the length of the hypotenuse divided by the length of the adjacent side. In a formula, it is abbreviated to just 'sec'.

Of the six possible trigonometric functions, secant, cotangent, and cosecant, are rarely used. In fact, most calculators have no button for them, and software function libraries do not include them.

They can be easily replaced with derivations of the more common three: sin, cos and tan.
Secant can be derived as the reciprocal of cosine:

Calculator

The inverse secant function - arcsec

For every trigonometry function such as sec, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. So the inverse of sec is arcsec etc. When we see "arcsec A", we interpret it as "the angle whose secant is A".

sec 60 = 2.000	Means: The secant of 60 degrees is 2.000
arcsec 2.0 = 60	Means: The angle whose secant is 2.0 is 60 degrees.

Sometimes written as asec or sec^-1

Angles greater than 90°

In a right triangle, the two variable angles are always less than 90° (See Interior angles of a triangle). But we can in fact find the secant of any angle, no matter how large, and also the secant of negative angles. For more on this see Secant definition for any angle.

Graph of the secant function

Because the secant function is the reciprocal of the cosine function, it goes to infinity whenever the cosine function is zero.

Other trigonometry topics

Angles

• Angle definition, properties of angles
• Standard position on an angle
• Initial side of an angle
• Terminal side of an angle
• Quadrantal angles
• Coterminal angles

Trigonometric functions

• Introduction to the six trig functions
• SOH CAH TOA memory aid


• Sine function (sin) in right triangles
• Graphing the sine function
• Sine waves


• Cosine function (cos) in right triangles
• Graphing the cosine function


• Tangent function (tan) in right triangles
• Graphing the tangent function


• Cotangent function cot (in right triangles)
• Secant function sec (in right triangles)
• Cosecant function csc (in right triangles)

Solving trigonometry problems

• The general approach
• Finding slant distance along a slope or ramp
• Finding the angle of a slope or ramp