We are asked to find the range of the function f(x)=\frac{\sin

Ellie Castro

Ellie Castro

Answered question

2022-04-22

We are asked to find the range of the function
f(x)=sinx132cosx2sinx,  for  0x2π

Answer & Explanation

Colonninisxi

Colonninisxi

Beginner2022-04-23Added 16 answers

Let y=sinx132sinx2cosx as the later is 0 where y0
Squaring both sides
(sinx1)2=y(32sinx2cosx)
sin2x+2(y1)sinx+1+y(2cosx3)=0
As sinx is real, the discriminant must be 0
i.e.,
(y1)21+y(2cosx3)
y[y(2cosx1)]0
As y0, this ymax(0,2cosx1)=1 if x=2nπ
y1y1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?