Understanding the Secant Function: How to Find the Value of sec(u) for a Given Angle

sec(u)

The term “sec(u)” refers to the secant function of the angle “u”

The term “sec(u)” refers to the secant function of the angle “u”. The secant function is defined as the reciprocal of the cosine function, so mathematically, we can write:

sec(u) = 1 / cos(u)

To find the value of sec(u) for a given angle “u”, we need to determine the cosine of that angle first.

Let’s take an example to illustrate this. Suppose we want to find the value of sec(45 degrees). First, we need to determine the cosine of 45 degrees.

cos(45 degrees) = √2 / 2

Now, we can substitute the cosine value into the secant function formula:

sec(45 degrees) = 1 / (√2 / 2)

To simplify further, we can multiply the numerator and denominator by the conjugate of the denominator (√2 / 2) to rationalize the denominator:

sec(45 degrees) = 1 * (2 / √2) / (1 * (√2 / 2))

sec(45 degrees) = 2 / √2

To rationalize the denominator, we multiply both the numerator and denominator by √2:

sec(45 degrees) = (2 / √2) * (√2 / √2)

sec(45 degrees) = 2√2 / 2

Finally, we simplify the expression:

sec(45 degrees) = √2

So, sec(45 degrees) = √2.

In summary, to find the secant of an angle “u”, find the cosine of that angle and take its reciprocal.

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