Tangent help...

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May 14th 2008, 11:29 AM
JT133

Tangent help...

Hi,
This is my first post and I'm really sort of stumped trying to do my homework here - it's to be in for tomorrow and I was out when it was being explained...

The sum is:

If tanA = -1, find the two values for angle A, where 0degrees <= A <= 360degrees

If anyone could explain how to do it, at Junior Cert level (Ireland), I'd really appreciate it!

I don't know how to get certain symbols (Doh)

Thanks in advance!
- JT
May 14th 2008, 11:39 AM
Moo

Hello,

Quote:

Originally Posted by JT133

Hi,
This is my first post and I'm really sort of stumped trying to do my homework here - it's to be in for tomorrow and I was out when it was being explained...

The sum is:

If tanA = -1, find the two values for angle A, where 0degrees <= A <= 360degrees

If anyone could explain how to do it, at Junior Cert level (Ireland), I'd really appreciate it!

I don't know how to get certain symbols (Doh)

Thanks in advance!
- JT

I'd do this way :

$\tan A=\frac{\sin A}{\cos A}$

--> $\sin A=-\cos A$ , right ?

~~~~~~~~~~~~
If you know your formulas, you know that this is true if and only if $\sin A=\pm \frac{\sqrt{2}}{2}$ (and $\cos A=\pm \frac{\sqrt{2}}{2}$ ).
Then see for which values A is such that :
- $\sin A=\frac{\sqrt{2}}{2} \text{ and } \cos A=-\frac{\sqrt{2}}{2}$

- $\sin A=-\frac{\sqrt{2}}{2} \text{ and } \cos A=\frac{\sqrt{2}}{2}$

Any question ? :)
May 14th 2008, 11:49 AM
xifentoozlerix

$\tan \frac{\pi } {4} = 1$ . This is a basic identity you should know.

Tangent is negative in the 2nd and 4th quadrant, so $\tan \left( {\pi - \frac{\pi }{4}} \right) = - 1$ and $\tan \left( {2\pi - \frac{\pi }{4}} \right) = - 1$ . Thus $\tan ^{ - 1} \left( { - 1} \right) = \frac{{3\pi }}{4},\frac{{7\pi }}{4}$ .
May 14th 2008, 12:06 PM
JT133

Thank you both for your replies, but in all honesty - I didn't understand a word you said..

I checked at the back of my book and the answers are 135degrees and 315degrees

I appreciate your answers but I think they're more leaving cert level (Thinking)

Any chance you can dumb them down to Honours level 15 year old maths (Rofl)
May 14th 2008, 12:10 PM
Moo

Quote:

Originally Posted by JT133

Thank you both for your replies, but in all honesty - I didn't understand a word you said..

I checked at the back of my book and the answers are 135degrees and 315degrees

I appreciate your answers but I think they're more leaving cert level (Thinking)

Any chance you can dumb them down to Honours level 15 year old maths (Rofl)

Why wouldn't we try ? :)

You HAVE to be familiar with specific values of sin and cos (and with tan, but you know that tan=sin/cos).

Here is a table you should know, it will really helps (Wink)

http://img127.imageshack.us/img127/1...tcircleoc9.gif
May 14th 2008, 12:28 PM
JT133

Well I can see that the answer is diagonally opposite on the table and I'm assuming that for example in the 135deg. that -rt2/2 is the sin value and rt2/2 is the cosine value for tan because Tan A = Sin A / Cos A and Sin A = - Cos A

I don't see how your getting that from the -1 though because Tan-1(-1) = -45

I've never been thought how to use tables for algebra just the trustworthy calculator way (Nod)
May 14th 2008, 12:29 PM
xifentoozlerix

Also, as a general rule:

$radians\cdot\frac{{180^ \circ }} {\pi } = degrees $

and

$degrees\cdot\frac{\pi } {{180^ \circ }} = radians $
May 14th 2008, 12:32 PM
xifentoozlerix

Quote:

Originally Posted by JT133

Well I can see that the answer is diagonally opposite on the table and I'm assuming that for example in the 135deg. that -rt2/2 is the sin value and rt2/2 is the cosine value for tan because Tan A = Sin A / Cos A and Sin A = - Cos A

I don't see how your getting that from the -1 though because Tan-1(-1) = -45

I've never been thought how to use tables for algebra just the trustworthy calculator way (Nod)

-45 degrees is the same thing as 315 degrees. If you go clockwise 45 degrees, it is the same thing as going counter-clockwise 315 degrees. However, -45 isnt between 0 and 360. Read up on period of trig functions on wikipedia or something.
May 14th 2008, 12:38 PM
Moo

Quote:

Originally Posted by xifentoozlerix

-45 degrees is the same thing as 315 degrees. If you go clockwise 45 degrees, it is the same thing as going counter-clockwise 315 degrees. However, -45 isnt between 0 and 360. Read up on period of trig functions on wikipedia or something.

In addition to xifentoozlerix's explanation, this is because cos, sin and tan are 360-periodic.

This means that $\cos (x+360k)=\cos(x)$ , $\sin (x+360k)=\sin x$ , $\tan (x+360k)=\tan x$

Where k is any integer (Wink)

I think that if you want real explanations, you should tell us what you've learnt about trigonometric functions :)
May 14th 2008, 12:49 PM
JT133

Okay well I think I'm getting it..

360 - 45 = 315 hence one of the answers

But 135... :confused:

Well this is my 1st year learning about trigonometry, I'd say from judging by your replies I only know the basics. I know that Sine = Opp/Hyp, Cosine = Adj/Hyp and Tangent = Opp/Adj

I haven't learned any formula on trigonometry except the Sine Rule and I've never had to use/or been thought about radians but I checked Wikipedia a minute ago

This is the level expected from me: http://examinations.ie/archive/examp...C003ALP2EV.pdf
(Question 5)

Thanks! :)
May 14th 2008, 01:17 PM
archer90

Tan(A) = -1
A = Tan^-1(-1) = -45 degrees

-45 isnt within your range of answers (0<A<360), but from this graph:
http://www.rockhounds.com/oplc/cd_on...ent_graph1.gif
(http://www.rockhounds.com/oplc/cd_on...ent_graph1.gif)
you can see that when the x value = -45, there are multiple x values that give the same y value, occurring every 180 degrees (the period of the tan graph).

To find the next value, add 180 to -45 (= 135, within the range).
To find the next value, add 180 to 135 (= 315, also within the range, although not on the diagram).

Hope this helps.
May 15th 2008, 07:30 AM
JT133

Ahhh! I get it! Thanks archer90, Moo and xifentoozlerix

Thats an extra 10 marks in my state exam, which is in 2 weeks!

:D
May 15th 2008, 08:17 AM
masters

Tan is negative in the 2nd Quadrant; thus
$\tan^-1 (-1) = \frac{3\pi}{4}$

$\frac{3\pi}{4}\cdot\frac{180}{\pi} = 135$