It is said that there are six ratios possible for the lengths of the sides of a right triangle. You have learned about the sine (sin), cosine (cos), and tangent (tan) ratios. The three other trigonometric ratios are their reciprocals.

Secant (sec): is the reciprocal of cosine, i.e. the ratio of the length of the hypotenuse to the length of the adjacent side.

sec θ = _1_ cosθ = hyp adj

Important note: There is a big difference between sec θ and cos^-1x. The first one means "1/cos θ". The second one involves finding an angle whose cosine is x. So on your calculator, don't use your cos^-1 button to find sec θ.

Find the value of secB

First find the length of the hypotenuse. Using the Pythagorean Theorem, or recognizing the Pythagorean Triple 5-12-13, the length of the hypotenuse is 13.

secB

=

13 5