Question

How do you sketch a right triangle corresponding to `cottheta=3/2` and find the third side, then find the other five trigonometric functions?

Answer 1

trigonometry ratio

Explanation:

cotangent is reffer to as the inverse of tangent
i.e tan B = opp/ Adj then
cot B = `1/"Adj" = "Adj"/"opp"`
`therefore cot theta = 3/2 = "adj"/"opp"`

`adj = 3 and opp = 2`

you can draw the triangle from there
then find the third side using pythagoras theorem
since the third side =`hyp = x`
therefore
`hyp^2 = opp^2 + Adj^2`

therefore #x^2 = 2^2 + 3^2

`x^2 = 4 + 9`

`x^2 = 13`
`x =sqrt13`