• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Finding Domain and Range of Functions

  • Thread starter MorganJ
  • Start date
Find the domain and range of y=sin^2x


I have a hard type computing this into my graphing calculator. Can someone help in the steps to find the domain?
 

rock.freak667

Homework Helper
6,230
27
y=sin2x=(sinx)2.

since it is squared it is never negative. The domain should be easy to find, given your knowledge of y=sinx
 
So the domain would be 0 less than or equal to positive infinity? and the range would be the same?
 

rock.freak667

Homework Helper
6,230
27
So the domain would be 0 less than or equal to positive infinity? and the range would be the same?
What is the domain of sin(x)? The range is the values of 'y' that the graph lies between.

You know that -1≤ sinx ≤ 1, so where would sin2x lie between?
 
the domain of sin (x) is -∞ < x < ∞ and would sin²x lie between -2 ≤ x ≤ 2...sorry i am bit confused.
 

rock.freak667

Homework Helper
6,230
27
the domain of sin (x) is -∞ < x < ∞
Right, sin2x has the same domain as sin(x)


and would sin²x lie between -2 ≤ x ≤ 2...sorry i am bit confused.[/QUOTE]


if y=sin2x, what is it's maximum and minimum value?
 
Wouldn't its maximum value be 1 and the minimum value be -1?
 
So...would it be 1 as well?
 
I have no clue, honestly. I am graphing it on my calculator. Would it be zero? I do not think the minimum value is a negative number.
 

rock.freak667

Homework Helper
6,230
27
I have no clue, honestly. I am graphing it on my calculator. Would it be zero? I do not think the minimum value is a negative number.
yes it would be zero.
 
Okay so the domain would be -∞ < x < ∞ and the range is 0 ≤ y ≤ 1 ?
 

rock.freak667

Homework Helper
6,230
27
Okay so the domain would be -∞ < x < ∞ and the range is 0 ≤ y ≤ 1 ?
That should be correct. You could write [itex] x \epsilon \Re[/itex] as well I believe.
 
Okay. Thank you so much for helping, rock.freak667. I really appreciate it :-)
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top