1. ## 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

- JT

2. Hello,

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

- 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 ?

3. $\tan \frac{\pi }
{4} = 1$
. 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 $\tan ^{ - 1} \left( { - 1} \right) = \frac{{3\pi }}{4},\frac{{7\pi }}{4}$.

4. 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

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

5. 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

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

6. 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

7. Also, as a general rule:

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

and

$degrees\cdot\frac{\pi }
$

8. 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
-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.

9. 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

I think that if you want real explanations, you should tell us what you've learnt about trigonometric functions

10. Okay well I think I'm getting it..

360 - 45 = 315 hence one of the answers

But 135...

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!

11. 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)
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.

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

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

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

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