Find the minum pts. in a trig equation

[misogynisticfeminist]

I have a trig equation with me

$$z=cos^2\theta+cos\theta+6$$

i am supposed to find the maximum and minimum points of z using completing the square.

I have found $$5\frac{3}{4}$$ as the minumum, but how do i go about finding the maximum?

 

[HallsofIvy]

The maximum is easy: the largest cos(θ) can possibly be is 1. What does that tell you?

 

[dextercioby]

It should come up to $2n\pi,n\in\mathbb{Z}$ for the maximum.

Daniel.

 

[dextercioby]

Hold on a second.Shouldn't the minimum be 4...?

Daniel.

 

[misogynisticfeminist]

ohhh sorry people, real sorry,

the equation should be,

$$cos^2\theta-cos\theta+6$$

its a minus cosine theta. I could get the minumum 5 3/4 but when i use cos theta=1, i get 6, not 8, that's where my problem comes in.

 

[HallsofIvy]

Ah- then you want cos(θ)= -1! Try that.

 

[misogynisticfeminist]

Ah- then you want cos(θ)= -1! Try that.

ohhh thanks a lot, that was useful !