sketch the graphs of y=cos2x & y=-0.5 over the domain-pi<_x<_pi use algebraic method to determine values of x where the graphs intersect.   

Expert Answers

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

`y = cos(2x)` and `y= -1/2`

Let's find the general solution in `-piltxltpi ` .

 

`cos(2x) = -1/2`

The primary solution for `(2x)` is,

`2x = cos^(-1)(-1/2)`

`(2x) = (2pi)/3`

 

The general solution for `cos(2x)` is given by,

`2x = 2npi+-(2pi)/3`

`x = npi+-pi/3` where `n in Z` .

 

For n= -1,

`x = -pi+-pi/3 `

The solution in the given range is `-pi+pi/3 = (-2pi)/3`

 

For n = 0,

`x = +-pi/3,`

The solutions in teh given range are, `pi/3` and `(-pi)/3` .

 

For n= 1,

`x = pi+-pi/3`

The solution in teh given range is,

x = pi-pi/3 = (2pi)/3

 

Therefore the solutions for x  in the given range are,

`x = (-2pi)/3` ,` x = (-pi)/3` ,` x =pi/3` and `x = (2pi)/3`

 

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial