Explain why the graph of y = 4 x </mrow> x

Hailie Blevins

Hailie Blevins

Answered question

2022-06-21

Explain why the graph of y = 4 x x 2 + 1 and y = 2 sin ( 2 arctan x ) are the same.

Answer & Explanation

scoseBexgofvc

scoseBexgofvc

Beginner2022-06-22Added 20 answers

take
x = tan α π 2 < α < π 2
so
y = 4 x x 2 + 1 = y = 4 tan α ( tan α ) 2 + 1 = 4 tan α 1 cos 2 α = 4 tan α . cos 2 α = 4 sin α cos α = 2 sin ( 2 α )
oleifere45

oleifere45

Beginner2022-06-23Added 3 answers

Since sin ( 2 A ) = 2 sin A cos A,
2 sin ( 2 arctan x ) = 4 sin ( arctan x ) cos ( arctan x ) = 4 ( x 1 + x 2 ) ( 1 1 + x 2 ) = 4 x 1 + x 2

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