Question

For the triangle shown, find sec x

Answer 1

You have the three basic trig functions: sine, cosine, and tangent.
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent

You have three other trig functions: secant, cosecant, and cotangent.
Cosecant = hypotenuse/opposite
Secant = hypotenuse/adjacent
Cotangent = adjacent/opposite

The way I’ve always remembered these is the 3 other trig functions are sine, cosine, and tangent flipped. Sine’s opposite is cosecant. Cosines opposite is secant, and tangents opposite is cotangent.

If you notice, each of these functions has a word starting with co-, and a word starting without co-. That’s how I’ve always remembered that sine goes to cosecant and cosine goes to secant.

Now that we know secant (or sec for short) x = hypotenuse/adjacent, you can find it.

First, find the hypotenuse of the triangle. Use Pythagorean’s theorem to do this.

a^2 + b^2 = c^2
5^2 + 7^2 = c^2
25 + 49 = c^2
c^2 = 74
c = √74

Now plug the values for hypotenuse and adjacent into sec(x)
sec(x) = √74/7