I need help with Math
I really just haven't done trig in a while, so I'm a little rusty...
I'm supposed to find the absolute extrema of y = (e^x)(sin(x)) in the interval
Extrema may occur in endpoints and at places where derivative is either zero or undefined, so I took the derivative
y' = (e^x(cos(x)) + e^x(sin(x)))
Factored
y' = e^x (cos(x) + sin(x))
This equation can never be undefined, and by looking at the separate factors, e^x can never be equal to 0
...but like I said, I haven't done trig in a while and I forgot what to do for cos(x) + sin(x) = 0
What do I do?
June 10, 2012
4 Comments • Newest first
[quote=Fiercerain]No! That is not how you do MATH, you look at the answer and settle for it. Do not question it.
OT: I'm kidding, that was harsh. This is how I reasoned the answer, I'm a bit rusty but.
Picture the radian circle, you'll want opposing values that sum to zero right? Such as +1 plus -1, or +10345 plus -10345. In this case, I referenced the radian circle for a radian that would give me identical X,Y coordinates that are opposite in sign. When factoring for trig functions, try to find a relationship between their function and respective coordinate on the radian circle.
i.e. Cos usually can be shortcut to reference X, Sin to reference Y, Tan to reference Y/X and so on.
Edit: Take @MellowYellow:'s advice.[/quote]
Ah, alright, I understand what you're saying.
Thanks for the help!
[quote=SunsetDews]Right, but how did you figure that out?
I'm interested in the approach more than anything[/quote]
No! That is not how you do MATH, you look at the answer and settle for it. Do not question it.
OT: I'm kidding, that was harsh. This is how I reasoned the answer, I'm a bit rusty but.
Picture the radian circle, you'll want opposing values that sum to zero right? Such as +1 plus -1, or +10345 plus -10345. In this case, I referenced the radian circle for a radian that would give me identical X,Y coordinates that are opposite in sign. When factoring for trig functions, try to find a relationship between their function and respective coordinate on the radian circle.
i.e. Cos usually can be shortcut to reference X, Sin to reference Y, Tan to reference Y/X and so on.
Edit: Take @MellowYellow:'s advice.
[quote=Fiercerain]Radians 3Pi/4 and 7Pi/4 would give you a sum of zero for the cos(x) + sin(x) factor.[/quote]
Right, but how did you figure that out?
I'm interested in the approach more than anything
Radians 3Pi/4 and 7Pi/4 would give you a sum of zero for the cos(x) + sin(x) factor.