Understanding the Secant Function: Definition, Properties, and Evaluation

secx

: sec(x)tan(x)

The function `sec(x)` is the reciprocal of `cos(x)`. It is defined as:

`sec(x) = 1/cos(x)`

Here, `x` represents the input angle in radians.

The function `sec(x)` is not defined for certain values of `x` where `cos(x)` equals zero. These values occur at odd multiples of π/2, i.e. π/2, 3π/2, 5π/2, etc.

The graph of `sec(x)` looks similar to the graph of `cos(x)`, with the exception that the function diverges to positive or negative infinity at the vertical asymptotes.

Some important properties of `sec(x)` include:

– Domain: all real numbers except odd multiples of π/2
– Range: (-∞,-1] U [1, ∞)
– Even function: `sec(-x) = sec(x)`
– Periodic function: `sec(x + 2π) = sec(x)`
– Trigonometric identity: `sec^2(x) – 1 = tan^2(x)`

To evaluate `sec(x)` for a particular value of `x`, we can use a calculator or reference a table of trigonometric functions.

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