# Trignometric functions and identities

1. Sep 25, 2013

### nil1996

1. The problem statement, all variables and given/known data
How to quickly solve problems on maximum and minimum values of trig functions with help of calculus:
Ex. 10cos2x-6sinxcosx+2sin2x

2. Relevant equations
none

3. The attempt at a solution
I know the method of simplification. But i want to do it quickly with calculus. How to do that??

Last edited: Sep 25, 2013
2. Sep 25, 2013

### HallsofIvy

Staff Emeritus
If you "want to do it quickly with calculus" then take the derivative, set the derivative equal to 0, and solve for x. However, the derivative is fairly complicated and I'm not sure this is "quicker" than just completing the square in the original.

Setting $f(x)= 10cos^2(x)- 6sin(x)cos(x)+ 2sin^2(x)$ then $f'(x)= -20cos(x)sin(x)- 6cos^2(x)+ 6sin^2(x)+ 4sin(x)cos(x)= -16sin(x)cos(x)- 6(sin^2(x)- cos^2(x))= 0$.

3. Sep 25, 2013

### nil1996

OK. but we get maximum values from that what about minimum values?