2. For `P(15,8)`, find value of all six trigonometric functions

Solution:
`P(15,8)`


Opposite side `(y)`, adjacent side `(x)` and hypotenuse `(r)`

`sin(theta), cos(theta), tan(theta)` fromula

`sin(theta) = "opposite"/"hypotenuse" = y/r`

`cos(theta) = "adjacent"/"hypotenuse" = x/r`

`tan(theta) = "opposite"/"adjacent" = y/x`

`csc(theta) = "hypotenuse"/"opposite" = r/y`

`sec(theta) = "hypotenuse"/"adjacent" = r/x`

`cot(theta) = "adjacent"/"opposite" = x/y`

Here `x=15` and `y=8`

In triangle ABC, by Pythagoras' theorem
`r^2 = x^2 + y^2`

`=15^2 + 8^2`

`=225 + 64`

`=289`

`:.r=sqrt(289)=17`

So, `x=15,y=8 and r=17`

`(1)` `sin(theta)=y/r=(8)/(17)=8/17`

`(2)` `cos(theta)=x/r=(15)/(17)=15/17`

`(3)` `tan(theta)=y/x=(8)/(15)=8/15`

`(4)` `csc(theta)=r/y=(17)/(8)=17/8`

`(5)` `sec(theta)=r/x=(17)/(15)=17/15`

`(6)` `cot(theta)=x/y=(15)/(8)=15/8`

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