# Find the minum pts. in a trig equation

• misogynisticfeminist
In summary, The conversation is about finding the maximum and minimum points of the trig equation z=cos^2\theta+cos\theta+6 using completing the square. The minimum value is found to be 5\frac{3}{4} and the maximum value is found to be 6 using cos(&theta;)=1. However, after correcting a mistake in the equation, the maximum value is found to be 8 using cos(&theta;)= -1.
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?

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

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

Daniel.

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

Daniel.

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.

Ah- then you want cos(&theta;)= -1! Try that.

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

ohhh thanks alot, that was useful !

## 1. What is a minimum point in a trigonometric equation?

A minimum point in a trigonometric equation is the lowest point on the graph of the equation. It is also known as the minimum value or the minimum vertex.

## 2. How do I find the minimum point in a trigonometric equation?

To find the minimum point in a trigonometric equation, you can use calculus techniques such as taking the derivative and setting it equal to zero. You can also use graphical methods by plotting the equation and identifying the lowest point on the graph.

## 3. Can there be more than one minimum point in a trigonometric equation?

Yes, there can be more than one minimum point in a trigonometric equation, depending on the equation and the range of the variables. In some cases, there may be multiple local minimum points but only one global minimum point.

## 4. How can I determine if a point is a minimum point in a trigonometric equation or not?

You can determine if a point is a minimum point in a trigonometric equation by evaluating the second derivative at the point. If the second derivative is positive, then the point is a minimum point. If the second derivative is negative, then the point is a maximum point.

## 5. Are minimum points important in trigonometric equations?

Yes, minimum points are important in trigonometric equations as they can help us determine the behavior of the equation and its graph. They can also be used in optimization problems to find the minimum or maximum value of a certain variable.

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