Question

A terminal ray passes through (12,-5). Fine the value to all six trig functions

Answer 1

Okay, here we have this:

Considering the provided angle, we are going to calculate the requested trigonometric functions, so we obtain the following:

So the first thing we will do is calculate the length of the hypotenuse, that is, the distance between the given point and the origin, then we have:

`\begin{gathered} r=√((12-0)^2+(-5-0)^2) \\ r=√(12^2+(-5)^2) \\ r=√(144+25) \\ r=√(169) \\ r=13 \end{gathered}`

Now we proceed to find the value of each ratio:

`sin\beta=(y)/(r)=(-5)/(13)`
`cos\beta=(x)/(r)=(12)/(13)`
`tan\beta=(y)/(x)=(-5)/(12)`
`csc\beta=(r)/(y)=(13)/(-5)=-(13)/(5)`
`sec\beta=(r)/(x)=(13)/(12)`
`cot\beta=(x)/(y)=(12)/(-5)=-(12)/(5)`