Circular Functions

1. Jan 16, 2010

TyErd

the equation 3sinx - 1 = b, where b is a positive real number, has one solution in the interval (0,2pi). The value of b is:

Frankly I have no idea where to even start with this problem.

2. Jan 16, 2010

tiny-tim

Hi TyErd!

(have a pi: π )

Hint: how many solutions in (0,2π) does 3sinx - 1 = 15 have?

And 3sinx - 1 = 0.5 ?

3. Jan 16, 2010

TyErd

Um. thnx for the pi. How do you know how many solutions there are?

4. Jan 16, 2010

tiny-tim

Draw a graph and find out.

Get on with it!

5. Jan 16, 2010

TyErd

alright i've drawn the graph, so what parts of the graph do i have to look at to know how many solutions there?

6. Jan 16, 2010

TyErd

hm..

7. Jan 16, 2010

Mentallic

Which parts? Umm...

If I asked you to find out how many solutions there are to $x^2=10$ how would you go about doing that by looking at a graph?

8. Jan 16, 2010

Staff: Mentor

And you should be looking only at the part of the graph on the interval [0, 2π].

9. Jan 16, 2010

tiny-tim

Nooo … (0,2π).

10. Jan 16, 2010

Staff: Mentor

Right, tiny-tim. I missed that it was the open interval.

11. Jan 16, 2010

TyErd

so when it says solutions, should i be looking at the x intercepts?

12. Jan 16, 2010

Staff: Mentor

What is the graph that you have drawn? Specifically, what is the formula of the function you have graphed?

13. Jan 16, 2010

TyErd

I tried to draw 3sinx-1=15 by taking 15 onto the other side but i've just realised that isnt right. How do you graph an equation that equals a number?

14. Jan 16, 2010

Mentallic

Graph $15=3sinx-1$
Then graph $y=15$

Do you see how if you tried to solve these two equations simultaneously, you would get $15=3sinx-1$?

Are there any intersections between the two functions?

Now, can you find any number b (such as 15) that makes it such that the equation $3sinx-1=b$ has only 1 real solution in the interval between 0 and 2π?
This is the same as saying for what number b will the function $y=b$ intersect the function $y=3sinx-1$ only once in the interval $(0,2\pi)$?

15. Jan 16, 2010

TyErd

Thankyouuu! i get it finally, you made it so much easier. thnx

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