4. Find the values of all six trigonometric functions for the given angle 90 deg

Solution:
`theta=90` (deg)

`theta=90^circ`

for `90^circ` the terminal side is the positive y-axis, so use the point `(0,1)`

So, we have
`x=0,y=1,r=1`

So, `x=0,y=1,r=1`


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)/(1)=1`

`(2)` `cos(theta)=x/r=(0)/(1)=0`

`(3)` `tan(theta)=y/x=(1)/(0)" is ""Undefined"`

`(4)` `csc(theta)=r/y=(1)/(1)=1`

`(5)` `sec(theta)=r/x=(1)/(0)" is ""Undefined"`

`(6)` `cot(theta)=x/y=(0)/(1)=0`

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