Can someone help me with Math

[Lillen]

I just started the D course in math in the communal adultschool here in sweden... I read it before but was instituionalized before I came to one quarter of the book.. The part handling trigonometery

Now i am limited to swedish facual languages in math so dont hang up on misconceptions and so on.

I wonder how i should think when i should show that cos^2v(tan^2v) +1 = 1 and such problems..

I knwo that i should make the most complicated side of the equal sign more easier and start there... How do i prove it to be correct? Sinus v and cosine v can take alot of values, so aren't there more then one way to solve these kinds of formulas (identities)?

 

[Tinker Grey]

The first thing to do is simplify. Usually, this can be accomplished by knowing what you would like to happen. In this case, cos(2v) * tan(2v) is kind of ugly. (I assume you meant that these 2 quantities are multiplied. In addition, I assume "^" means "of".)

Looking in your text book for various discusions of 'tan' should help. As it happens, I know that tan(x) = sin(x)/cos(x), so cos(2v)*tan(2v) = cos(2v)*sin(2v)/cos(2v) = sin(2v). Now, the problem is reduced to sin(2v) + 1 = 1. Subtracting 1 from both sides yields sin(2v) = 0.

Now, you can use your calculator to take the arcsine of both sides to find that 2v = 0. Under these conditions, we the only value for v is 0. However, you should memorize things like sin(0) = sin(180) = sin(-180) = 0. So your answer is that v can equal 0, 90 (half of 180) and -90 (half of -180).

 

[Blayz]

It is also more usual to describe -90 as +270...at least it was in my school
the ^ might have meant "squared", which devolves to

sin^2(v) = 1
sin(v) = +1 or -1
So v can be 90 or 270

 

[Tinker Grey]

I like your answer better.

It should be noted that most advanced math drops degrees and uses radians. In which case, the answer would be pi/2 and 3/2 * pi or -pi/2.

 

[driewerf]

I just started the D course in math in the communal adultschool here in sweden... I read it before but was instituionalized before I came to one quarter of the book.. The part handling trigonometery

Now i am limited to swedish facual languages in math so dont hang up on misconceptions and so on.

I wonder how i should think when i should show that cos^2v(tan^2v) +1 = 1 and such problems..

I knwo that i should make the most complicated side of the equal sign more easier and start there... How do i prove it to be correct? Sinus v and cosine v can take alot of values, so aren't there more then one way to solve these kinds of formulas (identities)?

Are you sure you copied the problem correctly?

Because this makes no sense. Slightly different:
cos[sup]2[/sup]v(tan[sup]2[/sup]v +1) = 1 This is an easy one.

writen tan[sup]2[/sup]v as sin[sup]2[/sup]v/cos[sup]2[/sup]v

bring cos[sup]2[/sup]v inside the (), you can cross the the two cos[sup]2[/sup]v, so remains
sin[sup]2[/sup]v+ cos[sup]2[/sup]v=1

which is indeed an identity.

 

[Lillen]

What??

I don't understand you?

Proving that sine of a value is something else is too hard for me to comprehand!

 

[Tinker Grey]

What is it you don't understand?

 

[driewerf]

I just started the D course in math in the communal adultschool here in sweden... I read it before but was instituionalized before I came to one quarter of the book.. The part handling trigonometery

Now i am limited to swedish facual languages in math so dont hang up on misconceptions and so on.

I wonder how i should think when i should show that cos^2v(tan^2v) +1 = 1 and such problems..

I knwo that i should make the most complicated side of the equal sign more easier and start there... How do i prove it to be correct? Sinus v and cosine v can take alot of values, so aren't there more then one way to solve these kinds of formulas (identities)?

First, Lillen, would you please check if you copied the problem correctly? Because written the way you did , it doesn't make much sense. Check especially whether yes or no the 1 is in the (...).


Written this way

cos[sup]2[/sup]v(tan[sup]2[/sup]v +1) = 1

it is much easier.

 

[Lillen]

Help me undestand periodic functions that are reformed with formulas? for instance, "sinx * cosx = 0"... the answer is 1 but i don't know how i get there...

I have trubble with factorise those equations, and see no whatsoever connections
when i follow already described equations in the book, i always note that a term is missing and have no clue were it went!

And also "^" in "^2" means square... and ^3 is a cube

PS: driewerf... i don't know, I forgot which page in the math book the problem was in!
I follow the first problem, i think i get a grip of it.. I understand it to some points... sin^2x + cos^2x = 1 can be rephrased to sin^2x = cos^2x -1

tan^2 x = sin^2 x / cos^2 x is also a relationship... i have accepted that.. or... is it tan x = sin x / cos x? both?

can't you exchange cos^2v ...+1 with sin^2v in cos^2v(tan^2v) + 1 = 1

But lets forget about identies, I understand what the book is telling me... lets go over to periodic equations that are reformed with formulas: here i need to be able to factorise as we were taught in course B, but in the book there is terms that are missing after setting x_1 = 0 or x_2 =0

As for radians, im there right now, but are doing a recap of the first chapter that were handling the above problem. pi radians = 180 degrees, one radian is the lenght of a radie in that circle (have no clue what its called in english).

 

[Lillen]

I got it... The book covers a formula for the dubble angle so i know were that missing term went...

 

[Tinker Grey]

As for radians, im there right now, but are doing a recap of the first chapter that were handling the above problem. pi radians = 180 degrees, one radian is the lenght of a radie in that circle (have no clue what its called in english).

I believe the word you are looking for is "radius".

I got it... The book covers a formula for the dubble angle so i know were that missing term went...

Congrats! Keep going.

 

[Lillen]

I believe the word you are looking for is "radius".

Radius then, and that circle is called unitcircle right???

Congrats! Keep going.

sin x * cos x = 0

sin x = 0 when x = 180 + n * 360???

cos x = 0 when x = 90/270 + n * 360???

Am i correct?

 

[Tinker Grey]

Radius then, and that circle is called unitcircle right???

I don't know what you mean by 'that' circle. A unit circle is when the radius is 1 (in whatever units are of interest).

sin x * cos x = 0

sin x = 0 when x = 180 + n * 360???

cos x = 0 when x = 90/270 + n * 360???

Am i correct?

Yes. When two things are multiplied, if either of them are zero the whole equation is zero. So, if sin(x) is zero then the equation is zero, or if cos(x) is zero then the equation is zero.

In some equations more than one part can be zero. However, in this case both parts depend on x. When sin(x) is zero, cos(x) cannot be.

You did miss something though. sin(x)=0 when x is 0 also. You've noted only the 180 case.

Also, I would not right my answer "90/270". It looks as if you are dividing 90 by 270. You might write "when x = 90 + n * 360, or 270 + n * 360".

In both cases you could be slightly more clever and write:
cos(x) = 0 when x = 0 + n * 180
sin(x) = 0 when x = 90 + n * 180

n * 180 would be stepping half-way around the circle for each n.

 

[Lillen]

Ahh... i think i understood you...

that aim circle you have a line you twist and rotate in trigonometery... were sin v = y value on its axis, and cos v = x value on its axis per definetion... what is it called in english..? translated directly from swedish it would've been unitcircle..?

Also, I would not right my answer "90/270". It looks as if you are dividing 90 by 270. You might write "when x = 90 + n * 360, or 270 + n * 360".

My bad...

 

[Tinker Grey]

Ahh... i think i understood you...

that aim circle you have a line you twist and rotate in trigonometery... were sin v = y value on its axis, and cos v = x value on its axis per definetion... what is it called in english..? translated directly from swedish it would've been unitcircle..?

I don't understand what's being said here.

Somebody else want to jump in?

 

[Lillen]

I missed the part were you confirmed that the unit circle is called the unit circle in english...

sin v i defined to be the y-coordinate in it and cos v is defined to be the x coordinate on it...

 

[Blayz]

It is called the unit circle in English, it is used to teach the basics of trigonometry but isn't really used outside of that, and yes it is used to show the projection if a line onto the x and y axes

 

[Lillen]

so using the unit circle as an assitant to solve the equation sin x * cos x = 0 show that were ever x in sin x = 0 cos x has to be 90+n*180?

Or am i using the unit circle the wrong way?

 

[Tinker Grey]

I missed the part were you confirmed that the unit circle is called the unit circle in english...

sin v i defined to be the y-coordinate in it and cos v is defined to be the x coordinate on it...

Yes, I believe that that is correct.

 

[Tinker Grey]

so using the unit circle as an assitant to solve the equation sin x * cos x = 0 show that were ever x in sin x = 0 cos x has to be 90+n*180?

Or am i using the unit circle the wrong way?

I believe you can do this. Where the unit circle crosses the Y-axis, cos(v) is 0. So, that is one of your answers. Where it crosses the X-axis, sin(v) is 0, that's another. Since there are 2 crossings of the Y-axis and 2 of the X, there are 4 answers, as we previously noted.