How to Calculate sec(π/3) and Understand the Secant Function

sec(π/3)

To calculate the value of sec(π/3), we first need to understand what secant is

To calculate the value of sec(π/3), we first need to understand what secant is.

The secant function (sec) is one of the trigonometric functions, and it is the reciprocal of the cosine function. Mathematically, it is defined as:

sec(x) = 1 / cos(x)

Here, x represents the angle in radians.

Now, let’s apply this definition to the given problem:

sec(π/3) = 1 / cos(π/3)

To find cos(π/3), we need to recall the unit circle or refer to the special triangles. In the case of π/3, it lies in the first quadrant of the unit circle and forms a 30-60-90 degree triangle. The cosine of π/3 is equal to the adjacent side length (which is 1) divided by the hypotenuse (which is 2).

cos(π/3) = 1/2

Now we can substitute this value back into the original equation:

sec(π/3) = 1 / cos(π/3) = 1 / (1/2) = 2

So, sec(π/3) is equal to 2.

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