Cos/Sin and Inclination Problems

So I'm taking pre-calc currently and I am incredibly stumped and in a hurry on these questions. I'd love some help with a detailed step process so I can understand it. Please and thanks!

1. Sketch y= -4+2 cos3(x-pi) Explain the amplitude, period, and translations.

I guess that because (y-k) is the standard equation for the problem that the -4 would mean it shifts down four units. My main problem with this is I've seen other problems where the number in front that's being added to the 2cos/sin3 problems is that it is usually the middle point of the max and min. Is that true for this one as the graph I'm provided does not indicate that it goes down that far. I have no idea what the translations mean. Also would x-pi mean that it shifts to the right one pi?

3. A reflector is attached to the front wheel of a bike 20 cm away from the center of the wheel. The diameter of the wheel and tube is 70cm. The bike is going 10 km/hr, express the height of the reflector above me the ground as a function of time. Assume time is t=0 seconds. Reflector starts at the highest point.

This question was probably the hardest for me. I understand that this would basically be a cosine graph starting at the top, I know the radius is 35 cm so the highest the reflec can go is 55 cm and the lowest it can go is 15cm. My only problem is how am I supposed to know how long the period is? I have all the numbers for the graph except for how long it takes a full revolution from the reflector to go from the top all the way around and back to the top.

Once again please and thanks!

Changelog:

1. Posted work

2. Solved #2 by myself.

Re: Cos/Sin and Inclination Problems

Quote:

Originally Posted by

**CorruptHope** So I'm taking pre-calc currently and I am incredibly stumped and in a hurry on these questions. I'd love some help with a detailed step process so I can understand it. Please and thanks!

1. Sketch y= -4+2 cos3(x-pi) Explain the amplitude, period, and translations.

2. Find inclination of 3x+5y=10. Give answer in degrees.

3. A reflector is attached to the front wheel of a bike 20 cm away from the center of the wheel. The diameter of the wheel and tube is 70cm. The bike is going 10 km/hr, express the height of the reflector abovn me the ground as a function of time. Assume time is t=0 seconds. Reflector starts at the highest point.

4.

√2cos x-1=0 Give answer in terms of pi.

5. sec²x=4 Give answer in terms of pi.

6. True/False, IF a line has inclination A and slope M, then M=tanA

7. True/False, Sin curves and cos curves are both called sine waves because vertical translations of each other.

Once again please and thanks!

I suggest you read the rules of the forum, taking particular note of the rules that state you should not post too many questions in a thread and that you need to show some effort.

Re: Cos/Sin and Inclination Problems

Quote:

Originally Posted by

**Prove It** I suggest you read the rules of the forum, taking particular note of the rules that state you should not post too many questions in a thread and that you need to show some effort.

My deepest apologies, please do not think that I have given my work to the internet to solve for me due to a lack of effort . I have my own work on each of these questions, but it is not right nor complete, which is why I asked for detailed step process. Please do not jump to assumptions that I have put no effort, there are sometimes more then one way to solve a math problem, which I would like to see.

As for the multiple problems, my mistake.

Re: Cos/Sin and Inclination Problems

Quote:

Originally Posted by

**CorruptHope** My deepest apologies, please do not think that I have given my work to the internet to solve for me. I have my own work on each of these questions, but it is not right or complete, which is why I asked for detailed step process. Please do not jump to assumptions that I have put no effort, there are sometimes more then one way to solve a math problem, which I would like to see.

As for the multiple problems, my mistake.

Then you need to post your work, then we can identify what you have done wrong and set you in the right direction.

Re: Cos/Sin and Inclination Problems

Quote:

Originally Posted by

**CorruptHope** So I'm taking pre-calc currently and I am incredibly stumped and in a hurry on these questions. I'd love some help with a detailed step process so I can understand it. Please and thanks!

1. Sketch y= -4+2 cos3(x-pi) Explain the amplitude, period, and translations.

Now in this problem I understand 2 is the amplitude and 3 is the period. I guess that because (y-k) is the standard equation for the problem that the -4 would mean it shifts down four units. My main problem with this is I've seen other problems where the number in front that's being added to the 2cos/sin3 problems is that it is usually the middle point of the max and min. Is that true for this one as the graph I'm provided does not indicate that it goes down that far. I have no idea what the translations mean. Also would x-pi mean that it shifts to the right one pi?

Edit: Posted my work on the problems[/FONT][/COLOR][/LEFT]

Well first of all, the period is not 3. The period of a trigonometric function of the form $\displaystyle \displaystyle \begin{align*} y = a\cos{\left[b\left(x - c\right)\right]} + d \end{align*}$ is $\displaystyle \displaystyle \begin{align*} \frac{2\pi}{b} \end{align*}$...

Re: Cos/Sin and Inclination Problems

Quote:

Originally Posted by

**Prove It** Well first of all, the period is not 3. The period of a trigonometric function of the form $\displaystyle \displaystyle \begin{align*} y = a\cos{\left[b\left(x - c\right)\right]} + d \end{align*}$ is $\displaystyle \displaystyle \begin{align*} \frac{2\pi}{b} \end{align*}$...

So that would mean that what I assumed the period to be is actually B so the real period is 2pi/3?

Re: Cos/Sin and Inclination Problems

Quote:

Originally Posted by

**CorruptHope** So that would mean that what I assumed the period to be is actually B so the real period is 2pi/3?

Yes

Re: Cos/Sin and Inclination Problems

It is not necessary to memorize a formula- except for memorizing that sine and cosine have period $\displaystyle 2\pi$. sin(a(x- b)) goes over one complete period when $\displaystyle a(x- b)$ goes from 0 to $\displaystyle 2\pi$. So solve a(x- b)= 0 and $\displaystyle a(x- b)= 2\pi$. Those give x= b/a for the first and $\displaystyle a= (b+ 2\pi)/a= b/a+ 2\pi/a$ for the second. The difference of the two numbers is $\displaystyle 2\pi/a$.