## sec(π/4)

### To find the value of sec(π/4), we need to recall the definition of secant

To find the value of sec(π/4), we need to recall the definition of secant.

Secant is a trigonometric function defined as the reciprocal of the cosine function. In other words, sec(x) is equal to 1/cos(x).

For our given angle of π/4, we need to find the value of cos(π/4) first. The cosine of π/4 can be determined by using the unit circle or trigonometric identity.

On the unit circle, when we move π/4 radians counter-clockwise, we end up at the point (√2/2, √2/2). The x-coordinate of this point gives us the value of cos(π/4).

Therefore, cos(π/4) = √2/2.

Now, we can calculate the value of sec(π/4) by taking the reciprocal of cos(π/4).

sec(π/4) = 1 / (√2/2).

To remove the fraction in the denominator, we multiply both the numerator and denominator by √2.

sec(π/4) = (1 / (√2/2)) * (√2/√2).

Simplifying the expression further, we get:

sec(π/4) = (2 / √2) * (√2/2).

The √2 in the numerator and denominator cancels out, leaving us with:

sec(π/4) = 2.

Therefore, the value of sec(π/4) is 2.

Note: It is always helpful to have a good understanding of basic trigonometric functions and identities to solve such problems.

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