Thread: Absolute extreme values of sin and cos

Hi there just wondering if someone could answer a question I have.
I've been given the function:

f(x)= cos x + sin x with a domain of [0,π] π <--- is pi (3.14)

and it wants me to determine the coordinates of the point where the tangent is horizontal.

I know first off I must take the derivative of this and I get

f ' (x)= cos x - sin x (i've just rearanged so the negative isn't infront)

0=cos x - sin x (set to zero)

sin x = cos x move sin over to make it equal

(sin x = cos x) / cos x divide both sides by cos

tan x = 1 this gives us the idenity (sinx/cosx =tanx) and 1


**this is where I get stuck I don't understand where I go from here to determine the coordinates if someone could show me it be much appreciated. Thank you

Originally Posted by darkfenix21

Hi there just wondering if someone could answer a question I have.
I've been given the function:

f(x)= cos x + sin x with a domain of [0,π] π <--- is pi (3.14)

and it wants me to determine the coordinates of the point where the tangent is horizontal.

I know first off I must take the derivative of this and I get

f ' (x)= cos x - sin x (i've just rearanged so the negative isn't infront)

0=cos x - sin x (set to zero)

sin x = cos x move sin over to make it equal

(sin x = cos x) / cos x divide both sides by cos

tan x = 1 this gives us the idenity (sinx/cosx =tanx) and 1


**this is where I get stuck I don't understand where I go from here to determine the coordinates if someone could show me it be much appreciated. Thank you

from the unit circle ...

at

Ahh that makes much more sense to me. I guess I went to far ahead with simplifying it for my own good.