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# tan of ugly angle in terms of tan of easy angle watch

1. Trying to explain something to a friend. Help me. I have no idea what is wrong. This is kind of a long thread cause I put all the conversation in. Would really appreciate it if you read though.
If anyone wants to type out an explanation for me to send to this friend, go ahead, I don't really want to anymore somehow.
The problem is basically: what's the tan of this angle?:

B:so if it was like

and it was like whats tan theta so do i just do tan of the small triangle thing then + pi/2?

A:well tanx = tan(x-180) by looking at the tan graph, which repeats every 180 So we can add 180 degrees to that angle, and take the tan of that instead

B:too confusing dont understand what youre saying

A:

angle there is x+180

B:but its not asking for that angle

A:Tan (that angle) is tan(theta)
they are the same

B: so i was supposed to move the graph sideways or what?

A:Yeah

B:..?

is not the same as

A:the tangent of both angles are the same though

B:the angles are DIFFERENT
****
i dont know why i ask you
forget it

A:Yes, the angles are different, but tan(angle1) = tan(angle2)

B: obviously if you say it once and i dont get it
if you say the same thing again
i am still not gonna get it
(insert more irrelevant conversation)

A:The quickest explanation is that the tan graph repeats every 180, hence tan{x}=tan{x+180}

B:what does that have to do
WITH ANYTHING?????

A: it means if we want tan{x} (theta=x for now) but x is hard to deal with, we can add 180 as many times as we want, and take the tan{ } of that instead.

Bk
what does that have to do with anything
ok if the component is (A,B) then what is the answer

A:
And the tan of that is op/adj which is easier
If the original vector was (a,b)
Then this vector is gonna be (-a,-b)
so b/a

B: ok so basically what i got out of what you said is

which i already know is wrong so thanks anyway

A:tan of ( ) = tan of ( )
so if the first angle is -120, then the second is -120+180=60
and tan(-120) = tan(60)

The rest is more swearing than explanation so I won't paste it in.

I just have no idea what else to say.

Thanks for reading. Yeah, I am kind of annoyed too. And this should probably go in health and relationships but I need actual maths people to read it.
2. Does he understand how to solve sinx = 0.5 for 0 <= x <= 180? If so, just tell him "you know how you do 180 - x to get the other angle? For tanx you just add or subtract 180".

And if you add or subtract 180 to theta in the diagram, it must end up in the 1st quadrant, where you can use opp/adj.
3. (Original post by Rabite)
Trying to explain something to a friend. Help me. I have no idea what is wrong. This is kind of a long thread cause I put all the conversation in. Would really appreciate it if you read though.
If anyone wants to type out an explanation for me to send to this friend, go ahead, I don't really want to anymore somehow.
The problem is basically: what's the tan of this angle?:

B:so if it was like

and it was like whats tan theta so do i just do tan of the small triangle thing then + pi/2?

A:well tanx = tan(x-180) by looking at the tan graph, which repeats every 180 So we can add 180 degrees to that angle, and take the tan of that instead

B:too confusing dont understand what youre saying

A:

angle there is x+180

B:but its not asking for that angle

A:Tan (that angle) is tan(theta)
they are the same

B: so i was supposed to move the graph sideways or what?

A:Yeah

B:..?

is not the same as

A:the tangent of both angles are the same though

B:the angles are DIFFERENT
****
i dont know why i ask you
forget it

A:Yes, the angles are different, but tan(angle1) = tan(angle2)

B: obviously if you say it once and i dont get it
if you say the same thing again
i am still not gonna get it
(insert more irrelevant conversation)

A:The quickest explanation is that the tan graph repeats every 180, hence tan{x}=tan{x+180}

B:what does that have to do
WITH ANYTHING?????

A: it means if we want tan{x} (theta=x for now) but x is hard to deal with, we can add 180 as many times as we want, and take the tan{ } of that instead.

Bk
what does that have to do with anything
ok if the component is (A,B) then what is the answer

A:
And the tan of that is op/adj which is easier
If the original vector was (a,b)
Then this vector is gonna be (-a,-b)
so b/a

B: ok so basically what i got out of what you said is

which i already know is wrong so thanks anyway

A:tan of ( ) = tan of ( )
so if the first angle is -120, then the second is -120+180=60
and tan(-120) = tan(60)

The rest is more swearing than explanation so I won't paste it in.

I just have no idea what else to say.

Thanks for reading. Yeah, I am kind of annoyed too. And this should probably go in health and relationships but I need actual maths people to read it.
Ok essentially, I got through most of it alright, you must know the CAST graph (all silver tea cups, sex and the city etc.) That's what it seems like you were trying to teach him. Remember everything works from the x axis. With east as 0 degrees and west as 180, it all depends on the direction which you turn, if you are going anticlockwise, that's positive, if you go clockwise, then you're heading negative. Say for example, you've got tan(225) = 1 (Because it's 45 degrees from the x axis in the T quadrant) is the same as tan(45) and is also the same as tan(-135). Yes, it repeats every 180 degrees, this is from the graph tan(x) which you should show. On the CAST graph, all the angles are NOT the same but they correlate to values on the tan(x) graph which all have the same value. The graph system is just a method of plotting the results from the tan(x) in an easy to use form because the tan(x) graph is regular. I'm hope this gives you some headway rather then causing you more ambiguity. I decided not to do it too algebraically because it seemed like you wanted something verbose.
4. This person is in university...why are they still on this crap in university...
thanks for the speedy replies. Said person is too annoyed to handle more than 30 seconds of thought right now.

I kinda just don't get why what I said was so unclear. I mean okay, this person replied each of my messages in under 30 seconds (I looked at the chat log) which possibly isn't enough time to take anything in...
5. Alright. In all honesty, I have always despised the unit circle / C.A.S.T Diagram. When it comes to the sort of trigonometric problems that you're referring to in your OP, I consult the standard sin, cos and tan graphs. That is, y = sin x, y= cos x and y = tan x.

Indeed, you are correct that the y = tan x function has a period of 180 degrees / 3.14159265358979 Rad. This is ever so easily viewed by the y = tan x graph. You don't need the C.A.S.T diagram to explain to your friend.

Of course, the C.A.S.T diagram has its uses. I use its principles when solving complex number functions within an Argand diagram. But personally I can solve trigonometric questions quicker using the y = tan x graph.

Hope i've helped.
6. (Original post by RBarack)
Alright. In all honesty, I have always despised the unit circle / C.A.S.T Diagram. When it comes to the sort of trigonometric problems that you're referring to in your OP, I consult the standard sin, cos and tan graphs. That is, y = sin x, y= cos x and y = tan x.

Indeed, you are correct that the y = tan x function has a period of 180 degrees / 3.14159265358979 Rad. This is ever so easily viewed by the y = tan x graph. You don't need the C.A.S.T diagram to explain to your friend.

Of course, the C.A.S.T diagram has its uses. I use its principles when solving complex number functions within an Argand diagram. But personally I can solve trigonometric questions quicker using the y = tan x graph.

Hope i've helped.
The OP doesn't need the CAST diagram to explain but it will be useful to his friend if he is to work with more trig functions. Of course, knowing where it comes from is paramount but the CAST diagram does speed up things compared to the graph, that's the point of it. YOU might be able to work with the tan(x) graph quicker but for someone who cannot visualise the tan(x) graph or even know it that well, it really isn't.

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