Question

If coto = 13 on top

6 on bottom


Then what is Seco


Remember to simplify and rationalize all answer

Answer 1

√(205)/13

Explanation:

You want sec(θ) when cot(θ) = 13/6.

Trig relations

Some calculators can figure this directly as ...

`\sec{(\cot^(-1)(13)/(6))}=\boxed{(√(205))/(13)}`

Others need to make use of the trig relations ...

tan(θ) = 1/cot(θ)

sec(θ) = √(tan²(θ) +1)

or

sec(θ) = 1/cos(θ)

Application

The tangent of the angle is

tan(θ) = 1/cot(θ) = 1/(13/6) = 6/13.

Then the secant is ...

sec(θ) = √((6/13)² +1) = √(6² +13²)/13

sec(θ) = √205/13

A calculator can get there from ...

sec(θ) = 1/cos(arctan(6/13)) = √205/13