1. Find the values of all six trigonometric functions for the given angle 225 degSolution:`theta=225` (deg)
`theta=225^circ`
We know that `225^circ=180^circ+45^circ`
Reference angle `=45^circ`
A 45-45-90 triangle is an isosceles right triangle, where the both legs are equal say `1` and the hypotenuse is `sqrt{2}`
`x=1,y=1,r=sqrt{2}`
`225^circ` is in Quadrant-3 and here x is -ve and y is -ve
So, `x=-1,y=-1,r=sqrt(2)`

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`
`(1)` `sin(theta)=y/r=(-1)/(sqrt(2))=(-sqrt(2))/2=-0.7071`
`(2)` `cos(theta)=x/r=(-1)/(sqrt(2))=(-sqrt(2))/2=-0.7071`
`(3)` `tan(theta)=y/x=(-1)/(-1)=1`
`(4)` `csc(theta)=r/y=(sqrt(2))/(-1)=-sqrt(2)=-1.4142`
`(5)` `sec(theta)=r/x=(sqrt(2))/(-1)=-sqrt(2)=-1.4142`
`(6)` `cot(theta)=x/y=(-1)/(-1)=1`