All Answers 359417 Answers

Wow Chris - Poor Fortun will think he is supposed to memorise all that!!

The unit circle is very useful but mostly just for

0, pi/2, pi, and 3pi/2 radians and multiples of these of course.

Are you really up for a full scale lesson here Fortun.  

If you get me and probably Chris reved up you may not be able to stop us lol.

Or have you learned enough for the moment.   You can ask for more help whenever you want it either way.    

Wow you guys are good.Thanks sooooo much!!!!No seriously,thanks so much.Av been stumped by this for quite a while n every other math site assumes i know trig already..lol.Thanks guys!!!!!!!!!

Here's something else that might help....the unit circle....

I do not memorise ANY of them.  I just understand them!

The values generated by these solutions are ones associated with the pretty common "reference" angles  in the first quadrant [0, pi/6, pi/4, pi/3 and pi/2]....you should commit these to memory.......and then, be able to apply them in any of the other 3 quadrants....this is a VERY important trig topic....!!!

No you don't have to memorise anything.  Well not much anyway. lol

here is your equation

2cosΘsinΘ=cosΘ where [0,2π)

take it all to one side

2cosΘsinΘ-cosΘ=0 

factorise

cosΘ(2sinΘ-1)=0 

now  this will only be true if one of the factors =0

ie

cosΘ=0           $$\theta = \pi/2 \;\;or\;\; 3\pi/2$$

or

2sinΘ-1=0           $$sin\theta=1/2$$          $$\theta = \pi/6\;\;or\;\;5\pi/6$$        

so

$$\theta = \pi/2 \;\;or\;\; 3\pi/2$$    $$\;\;or\;\;\pi/6\;\;or\;\;5\pi/6$$

Now if you are still having problems please try and tell us what you do not understand. 

Probably but then again maybe they want the set of all circles that pass through those points or maybe they want something else.  

I think this person wants to write an equation of a line using these points...

OK....let's get the slope, first   ....where the slope, m, is defined as   change in y / change in x

And from the first point to the second, y changes by -1

And from the first point to the second, x changes by - 9

So...the slope is  -1 / -9  = 1/9    ....and we can use one of the points to write the equation...I'll use the first one ...  so we have

y - 4  = (1/9)(x -5)     simplify the right side and add 4 to both sides

y = (1/9)x - 5/9 + 4

y = (1/9)x + 31/9

Thanks @CPhill.Appreciate your quick responsesThanks for the welcome@Melody.Ok so could you dumb it down a little for me?Are these graph values constant so I just have to memorize the graph or they have to be worked out every single time?

Thanx.....!!!

I really like the question too.  You were asking us to help you understand.  

We really like such questions.  

Thank you  fortun and welcome to Web2 forum.     

Nice answer Chris  

We might suck.....but.......at least we know how to convert decimals to fractions.....

I have a tip for you......never complain about the service in a restaurant UNTIL AFTER the food is served.....!!!

Well I think the speed would be the dependant variable.

That is it would depend on the height of the roller coaster.

So I would put height on the horizontal axis and speed on the vertical axis.

so the domain would be height    [20,205]   in feet

and the range would be speed     [0,75]      in miles/hour

If you do not ask then you will not get help.

If you do ask then you may get help.

You decide  

2cosΘsinΘ=cosΘ     subtract cosΘ from each side

2cosΘsinΘ - cosΘ  = 0      factor

cosΘ (2sinΘ - 1) = 0

And setting each factor to 0, we have

cosΘ = 0  and this happens at pi/2 and 3pi/2 

And     

sinΘ = 1/2    and this happens at pi/6 and 5pi/6

It looks like you just included the first quadrant values in your solution......

I think you got a bit muddled there Tetration.  

$$\\FV=10000(1+0.07)^5\\
FV=10000(1.07)^5\\$$

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{{\mathtt{1.07}}}^{{\mathtt{5}}} = {\mathtt{14\,025.517\: \!307}}$$

$14,025.51

what equation?  You have just got two points there.   

Yea we sux.     

Did your rudeness help you get your question answered?      

$$5.3\times 10^{-3}$$

would be entered as 

5.3*10^(-3)

4 hours =4*60=240 minutes

so it will be

240/3

Hint look for a square number that goes into 45

square numbers are

1*1=2

2*2=4

3*3=9

etc

Tell me what the square number is that goes into 45 and we will take it from there.

you forgot the Bio  lol 

I've never done that with Desmos before.  Thanks Chris,

thank you for showing me this feature.  I will make good use of it.    

No it does not simplify to a number!