3. For `P(-8,6)`, find value of all six trigonometric functions

Solution:
`P(-8,6)`


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=-8` and `y=6`

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

`=(-8)^2 + 6^2`

`=64 + 36`

`=100`

`:.r=sqrt(100)=10`

So, `x=-8,y=6 and r=10`

`(1)` `sin(theta)=y/r=(6)/(10)=3/5=3/5`

`(2)` `cos(theta)=x/r=(-8)/(10)=(-4)/5=-4/5`

`(3)` `tan(theta)=y/x=(6)/(-8)=(-3)/4=-3/4`

`(4)` `csc(theta)=r/y=(10)/(6)=5/3=5/3`

`(5)` `sec(theta)=r/x=(10)/(-8)=(-5)/4=-5/4`

`(6)` `cot(theta)=x/y=(-8)/(6)=(-4)/3=-4/3`

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