Question

Find the value of the expression in terms of x, with the help of a reference triangle

sin (cos^–1(1 – x))

Answer 1

sin (cos^–1(1 – x)) = `sin[cos^-1 ("Adj"/"Hyp")]`

`[because cos ("Adj"/"HyP") = (1 - x)/1]`

Adj = 1 – x

Hyp = 1

Opp = `sqrt(1^2 - (1 - x)^2`

= `sqrt(1 - (1 + x^2 - 2x))`

= `sqrt(1 - 1 - x^2 + 2x)`

= `sqrt(2x - x^2`

`sin("Opp"/"Hyp") = sqrt(2x - x^2)/1`

= `sqrt(2x - x^2)`