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sec

Symbolic secant function

Syntax

Description

example

sec(X) returns the secant function of X.

Examples

Secant Function for Numeric and Symbolic Arguments

Depending on its arguments, sec returns floating-point or exact symbolic results.

Compute the secant function for these numbers. Because these numbers are not symbolic objects, sec returns floating-point results.

A = sec([-2, -pi, pi/6, 5*pi/7, 11])
A =
   -2.4030   -1.0000    1.1547   -1.6039  225.9531

Compute the secant function for the numbers converted to symbolic objects. For many symbolic (exact) numbers, sec returns unresolved symbolic calls.

symA = sec(sym([-2, -pi, pi/6, 5*pi/7, 11]))
symA =
[ 1/cos(2), -1, (2*3^(1/2))/3, -1/cos((2*pi)/7), 1/cos(11)]

Use vpa to approximate symbolic results with floating-point numbers:

vpa(symA)
ans =
[ -2.4029979617223809897546004014201,...
-1.0,...
1.1547005383792515290182975610039,...
-1.6038754716096765049444092780298,...
225.95305931402493269037542703557]

Plot Secant Function

Plot the secant function on the interval from -4π to 4π.

syms x
fplot(sec(x),[-4*pi 4*pi])
grid on

Handle Expressions Containing Secant Function

Many functions, such as diff, int, taylor, and rewrite, can handle expressions containing sec.

Find the first and second derivatives of the secant function:

syms x
diff(sec(x), x)
diff(sec(x), x, x)
ans =
sin(x)/cos(x)^2
 
ans =
1/cos(x) + (2*sin(x)^2)/cos(x)^3

Find the indefinite integral of the secant function:

int(sec(x), x)
ans =
log(1/cos(x)) + log(sin(x) + 1)

Find the Taylor series expansion of sec(x):

taylor(sec(x), x)
ans =
(5*x^4)/24 + x^2/2 + 1

Rewrite the secant function in terms of the exponential function:

rewrite(sec(x), 'exp')
ans =
1/(exp(-x*1i)/2 + exp(x*1i)/2)

Evaluate Units with sec Function

sec numerically evaluates these units automatically: radian, degree, arcmin, arcsec, and revolution.

Show this behavior by finding the secant of x degrees and 2 radians.

u = symunit;
syms x
f = [x*u.degree 2*u.radian];
secf = sec(f)
secf =
[ 1/cos((pi*x)/180), 1/cos(2)]

You can calculate secf by substituting for x using subs and then using double or vpa.

Input Arguments

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Input, specified as a symbolic number, variable, expression, or function, or as a vector or matrix of symbolic numbers, variables, expressions, or functions.

More About

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Secant Function

The secant of an angle, α, defined with reference to a right angled triangle is

sec(α)=1cos(α)=hypotenuseadjacent side=hb.

The secant of a complex argument, α, is

sec(α)=2eiα+eiα.

See Also

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Introduced before R2006a