Question

How do you figure out the csc and sec? For a standard-position angle determined by the point (x, y), what are the values of the trigonometric functions?

For the point (9, 12), find csc theta and sec theta

Answer 1

`cosec{\theta}=(15)/(12)` and
`sec{\theta}=(15)/(9)`

Explanation:

For the standard position triangle having sides of x=9 and y=12 and the included theta, the hypotenuse can be calculated through the Pythagorean theorem such as:

`(AC)^2=(AB)^2+(BC)^2`

`(AC)^2=144+81`

`(AC)^2=225`

`AC=15`

Therefore, the value of AC(Hypotenuse) is 13 units.

Now,
`cosec{\theta}=(AC)/(AB)`

`cosec{\theta}=(15)/(12)`

and
`sec{\theta}=(AC)/(BC)`

`sec{\theta}=(15)/(9)`

which are the required values of
`cosec{\theta}` and
`sec{\theta}`.