Calculate Sec 4 Degrees 50 15

What is the secant function?

The secant function, often written as sec(θ), is one of the six primary trigonometric functions. It's defined as the reciprocal of the cosine function:

The secant function is periodic with a period of 360°, meaning it repeats its values every full rotation. It's positive in the first and fourth quadrants and negative in the second and third quadrants.

How to calculate secant

To calculate the secant of an angle:

1. Convert the angle from degrees, minutes, and seconds to decimal degrees if needed
2. Calculate the cosine of the angle
3. Take the reciprocal of the cosine value to get the secant

This calculator handles these steps automatically for you.

Secant formula

The formula shows that the secant is simply the reciprocal of the cosine. This relationship is fundamental in trigonometry and makes calculations straightforward once you have the cosine value.

Worked example

Let's calculate sec(4°50'15") step by step:

1. Convert 4°50'15" to decimal degrees:
   • Degrees: 4
   • Minutes to degrees: 50/60 ≈ 0.8333
   • Seconds to degrees: 15/3600 ≈ 0.0042
   • Total: 4 + 0.8333 + 0.0042 ≈ 4.8375°
2. Calculate cos(4.8375°):
   • Using a calculator: cos(4.8375°) ≈ 0.9986
3. Calculate sec(4.8375°):
   • sec(4.8375°) = 1 / 0.9986 ≈ 1.0014

The result is approximately 1.0014, which means the secant of 4°50'15" is about 1.0014.