sec(x)
sec(x)tan(x)
The secant function of x, denoted as sec(x), is defined as the reciprocal of the cosine function of x, denoted as cos(x). In other words,
sec(x) = 1/cos(x)
For any value of x other than the values where cosine is equal to zero (nπ/2 for all integers n), the secant function is defined and takes real values.
To compute the value of sec(x), you can use either a calculator or know the values of the cosine function at specific angles. Some common values of sec(x) include:
– sec(0) = 1
– sec(π/6) = 2/√3
– sec(π/4) = √2
– sec(π/3) = 2
– sec(π/2) is undefined
It’s also worth noting that the secant function is an even function, meaning that it’s symmetric with respect to the y-axis. In other words,
sec(-x) = sec(x) for all x
Additionally, the secant function has many important properties in trigonometry and calculus, including its relationship with the tangent and the derivative of the secant function, which is equal to the secant function multiplied by the tangent function at the same angle:
d/dx(sec(x)) = sec(x)tan(x)
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