Need Urgent Math Help: Trigonometry Questions Review

[majormuss]

Homework Statement

Hi guys,
I was working on some few Trigonometric questions and since my book doesn't have an answer sheet, I thought it would be a good idea to scan it and then upload so I someone could review my answers and tell me where I went wrong. There are 14 questions but I left some blank because I didn't get what they were asking... Please correct my mistakes and reply so I can understand better.

Homework Equations

The Attempt at a Solution

http://www.facebook.com/?sk=media#!/photo.php?pid=1254245&id=1371620807

 

[vela]

Can you put it somewhere that doesn't require one to register with Facebook to see it?

 

[majormuss]

Can you put it somewhere that doesn't require one to register with Facebook to see it?

Urghh.. I didn't know it would happen that way.. Do you have any suggestions as where or how I can upload the page??

 

[gain01]

You didn't put an answer for 1. What is sin(3pi/2)? What is cos(3pi/2)? What is cos(0) and sin(0)? 2. Is wrong? The sine function max is 1 and min is -1. So 5+2*(-1)=3. 3. Not the y-axis. Sin(pi/2)=1;whereas sin(-pi/2)=-1. So symmetric with the origin. Being symmetric with the origin means f(-x)=-f(x). 4. Correct. 5. The question was what x value, not what is the minimum value. -3 is incorrect. 6. Correct

 

[gain01]

8. Correct
9. Correct
10. Correct
11. Max of cosine is 1 and min is -1. Use that to answer this question.
12. When x=pi, it reaches it's max. Minimum of sine is -1. When is sine -1?
13. If the function was 2/3sin(theta), then it would be 1 cycle. If it was 2/3sin(2*theta), then it would be 2 cycles. But instead it 2/3sin(4*theta). So how many cycles?
14. Correct

 

[vela]

Urghh.. I didn't know it would happen that way.. Do you have any suggestions as where or how I can upload the page??

You should be able to attach it to a post here. Click the "manage attachment" button. You may have to go to the advanced options to see it.

 

[majormuss]

You should be able to attach it to a post here. Click the "manage attachment" button. You may have to go to the advanced options to see it.

Thanks...needed that I will try posting it again. ( someone already posted answers to questions 8-14)

 

[majormuss]

8. Correct
9. Correct
10. Correct
11. Max of cosine is 1 and min is -1. Use that to answer this question.
12. When x=pi, it reaches it's max. Minimum of sine is -1. When is sine -1?
13. If the function was 2/3sin(theta), then it would be 1 cycle. If it was 2/3sin(2*theta), then it would be 2 cycles. But instead it 2/3sin(4*theta). So how many cycles?
14. Correct

Question 11- i figured my amplitude was '4' and so the range should be -4$$\subseteq$$y$$\subseteq$$4,... why is it not?

 

[majormuss]

Page re-posted

Homework Statement

I re-posted the questions from the previous post... The only questions I ma still confused about is 7, 11 and please someone check 1- 6..

Homework Equations

The Attempt at a Solution

 

[gain01]

The amplitude is 3. Max of cos2x is 1 and min of cos2x is -1. So max of y = (3*1+1) & min of y = (3*-1+1). The other answer are posted above 8-14 posting.

 

[zooxanthellae]

For 11., it may help to think that $$z = 2x$$. Then we can re-write the function as $$y = 3cos(z) + 1$$. What would the maximum and minimum values for the function $$cos(z)$$ be? Considering that, what would the maximum and minimum values of $$3cos(z)$$ be? Then you just add 1 to both of those to get the answer.

(Do you understand why for a problem like this, you could have replaced 2x with anything and gotten the same answer? No matter if you're dealing with cos(4a) or cos(7d) or cos(6b), the function has a maximum of 1 and minimum of -1.)

 

[majormuss]

Did you get the answer for number 1? I still coudln't figure it out. For # 2, the correct answer is 3.

The answer to number 1 is (3)
Just refer to the Unit Circle- Check the IV Quadrant and notice as the cos or "x value" changes
as the angle approaches 360 degree line.
And how did you get 3 for number 2?? I still think its "4"

 

[zooxanthellae]

majormuss: look at Question 2 again. It asks "What is the minimum element in the range of the equation $$y = 5 + 2sin\theta$$?" In other words, what is the lowest y-value for this function? Well, you know that the sine function goes from -1 to 1, and therefore has a minimum of -1. Knowing this, what would the minimum of the function $$2sin\theta$$ be?

Then since the function is $$y = 5 + 2sin\theta$$, you would add 5 to the minimum of $$2sin\theta$$ (since $$y = 5 + 2sin\theta$$ is the same as $$y = 2sin\theta + 5$$) to get the minimum of $$y = 5 + 2sin\theta$$.

 

[majormuss]

majormuss: look at Question 2 again. It asks "What is the minimum element in the range of the equation $$y = 5 + 2sin\theta$$?" In other words, what is the lowest y-value for this function? Well, you know that the sine function goes from -1 to 1, and therefore has a minimum of -1. Knowing this, what would the minimum of the function $$2sin\theta$$ be?

Then since the function is $$y = 5 + 2sin\theta$$, you would add 5 to the minimum of $$2sin\theta$$ (since $$y = 5 + 2sin\theta$$ is the same as $$y = 2sin\theta + 5$$ to get the minimum of $$y = 5 + 2sin\theta$$.

oh yes... I get your point...the answer is 3 ... thanks a lot!