Hi, can someone please explain how to solve the problem below.

Find the maximum value of 3sinx + cos2x.

Your help is very much appreciated.

Printable View

- August 2nd 2012, 07:28 AMshiny718max value of trigonometric function
Hi, can someone please explain how to solve the problem below.

Find the maximum value of 3sinx + cos2x.

Your help is very much appreciated. - August 2nd 2012, 08:04 AMDagger2006Re: max value of trigonometric function
There are a few ways. If you know calculus, take the derivative and find the critical points.

If you don't know calculus. You can also graph the equation either by hand with several test test points or with a graphing utilitiy.

If you prefer to not graph it, you can do some critical thinking. For example, on the interval from x=0 to x = pi/2, you have 3sinx going from 0 to 3. On this same interval you have cos2x going from 1 to -1. Thus you can determine which one changes value faster. Then use that information to figure out at what angle the fastest growing function stop growing. - August 2nd 2012, 08:04 AMskeeterRe: max value of trigonometric function
- August 2nd 2012, 08:16 AMHallsofIvyRe: max value of trigonometric function
**If**that were "3 cos(x)+ 2sin(x)" you could use r sin(x+ a)= r sin(a)cos(x)+ r cos(a)sin(x) and look for a and r so that r cos(a)= 3, r, sin(a)= 2 and . (I say this because I misread the problem and started to do it that way!)

But with "3 cos(x)+ sin(2x)" I see no method simpler than taking the first derivative and setting it equal to 0- a "Calculus" rather than "Trigonometry" method. - August 2nd 2012, 08:21 AMProve ItRe: max value of trigonometric function
- August 3rd 2012, 06:15 AMshiny718Re: max value of trigonometric function
Thanks a lot! :)