Question

For a standard position angle determined by the point (x,y) what are the values of the trigonometric functions?

For te point (5,12), find csc theta and sec theta

Answer 1

`cosec{\theta}=(13)/(12)` and
`sec{\theta}={(13)/(5)}`

Explanation:

For the standard position triangle having sides of x=5 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+25`

`(AC)^2=169`

`(AC)=13`

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

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

⇒
`cosec{\theta}=(13)/(12)`

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

⇒
`sec{\theta}={(13)/(5)}`

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

Answer 2

For the standard position triangle having sides of x=5 and y=12 and the included theta, the hypotenuse can be estimated through the pythagorean theorem and is equal to 13, with this sin theta equals 12/13 and cosine theta = 5/13, since csc theta = 1/sin theta and sec theta = 1/cos theta, therefore, csc theta = 13/12 and sec theta = 13/5