y=sin(2 cot^(-1) x)

Question

Draw the Graph, find Domain and Range, also find an equivalent formula

Answer 1

Given Sin(2cot^(-1)x

Let the right angle triangle sides are 1,x,sqrt(1-x^2).

From the pythagerons therom

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

1 = x^2+1-x^2

1 = 1

we know that tanx = opposite side/adjacent side

tanx = x/sqrt(1-x^2)

Now y = Sin(2cot^(-1)x

y = Sin(2tanx)

y = Sin(2x/sqrt(1-x^2))

Graph of the y = Sin(2x/sqrt(1-x^2))

Domain of sine functions is all real numbers and range is {y/-1<y<1}