Trigonometric integrals

[jpanknin]

I'm working on trigonometric integrals and there are two methods for representing [imath]\sin^{2}\{x\}[/imath].

One is the Pythagorean method [math]\{1-cos^2{x}\}[/math] and the other is the half-angle formula [math]\frac{1}{2}(1-cos2x)[/math]
Same thing for [imath]\cos^{2}\{x\}[/imath].

How do you know when to use the pythagorean approach vs. the half-angle approach? The textbook we're using uses the pythagorean method for one replacement and then says the half-angle method is easier for a different problem, but doesn't explain why.

 

[Dr.Peterson]

I'm working on trigonometric integrals and there are two methods for representing [imath]\sin^{2}\{x\}[/imath].

One is the Pythagorean method [math]\{1-cos^2{x}\}[/math] and the other is the half-angle formula [math]\frac{1}{2}(1-cos2x)[/math]
Same thing for [imath]\cos^{2}\{x\}[/imath].

How do you know when to use the pythagorean approach vs. the half-angle approach? The textbook we're using uses the pythagorean method for one replacement and then says the half-angle method is easier for a different problem, but doesn't explain why.

Please show us those two examples.

Also, please try using the other method on each of them, so you can discover for yourself how they do not work! This will benefit you far more than being told.

In general, in solving any problem you look for methods that will advance you toward your goal. How that happens will vary. Sometimes, you just have to try things until you find one that works!