Question

How do you find the values of the other five trigonometric functions of the acute angle A with `cscA=3`?

Answer 1

`sinA=1/3`

`cosA=(2sqrt2)/3`

`tanA=1/(2sqrt2)`

`cscA=3/1`

`secA=3/(2sqrt2)`

`cotA=2sqrt2/1`

Explanation:

`cscA=3`
`cscA="hypotenuse"/"opposite side"=3/1`

By pythagoras theorem

`"adjacent side"=sqrt(3^2-1^2)=2sqrt2`

We have

`"opposite side"=1`
`"adjacent side"=2sqrt2`
`"hypotenuse"=3`

`sinA="opposite side"/"hypotenuse"=1/3`
`cosA="adjacent side"/"hypotenuse"=(2sqrt2)/3`
`tanA="opposite side"/"adjacent side"=1/(2sqrt2)`
`cscA="hypotenuse"/"opposite side"=3/1`
`secA="hypotenuse"/"adjacent side"=3/(2sqrt2)`
`cotA="adjacent side"/"opposite side"=2sqrt2/1`