Solve the equation on the interval  x is greater than 0 an less than 2pi sin(2x-pi/2)=1 Please show step by step instructions.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You should solve the equation using the followings such that:

`sin x = a => x = (-1)^n arcsin a + npi`

Reasoning by analogy yields:

`sin(2x-pi/2)=1 => 2x-pi/2 = (-1)^n arcsin 1 + npi`

`2x - pi/2 = (-1)^n*pi/2 + npi`

`2x = (-1)^n*pi/2 + npi + pi/2`

`x = (-1)^n*pi/4 + npi/2 + pi/4`

For `n = 1 => x = -pi/4 + pi/2 + pi/4 = pi/2`

For `n = 2 => x = pi/4 + pi + pi/4 => x = pi/2 + pi = 3pi/2`

For `n = 3 =>x = -pi/4 + 3pi/2 + pi/4 = 3pi/2`

` n = 4 => x = pi/4 + 2pi + pi/4`

Notice that for `n = 4 => x = 5pi/4 > 2pi`

Hence, evaluating the solutions to the given equation, in `(0,2pi),`  yields `x = pi/2`  and `x = 3pi/2` .

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial