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Thread: Tangent help...

  1. #1
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    Smile 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

    Thanks in advance!
    - JT
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  2. #2
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    Hello,

    Quote Originally Posted by JT133 View Post
    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

    Thanks in advance!
    - JT
    I'd do this way :

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

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

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

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


    Any question ?
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  3. #3
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    $\displaystyle \tan \frac{\pi }
    {4} = 1$. This is a basic identity you should know.

    Tangent is negative in the 2nd and 4th quadrant, so $\displaystyle \tan \left( {\pi - \frac{\pi }{4}} \right) = - 1$ and $\displaystyle \tan \left( {2\pi - \frac{\pi }{4}} \right) = - 1$. Thus $\displaystyle \tan ^{ - 1} \left( { - 1} \right) = \frac{{3\pi }}{4},\frac{{7\pi }}{4}$.
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  4. #4
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    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
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  5. #5
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    Quote Originally Posted by JT133 View Post
    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


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  6. #6
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    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
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  7. #7
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    Also, as a general rule:

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

    and

    $\displaystyle degrees\cdot\frac{\pi }
    {{180^ \circ }} = radians
    $
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  8. #8
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    Quote Originally Posted by JT133 View Post
    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.
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  9. #9
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    Quote Originally Posted by xifentoozlerix View Post
    -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 $\displaystyle \cos (x+360k)=\cos(x)$, $\displaystyle \sin (x+360k)=\sin x$, $\displaystyle \tan (x+360k)=\tan x$

    Where k is any integer



    I think that if you want real explanations, you should tell us what you've learnt about trigonometric functions
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  10. #10
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    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!
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  11. #11
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    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.
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  12. #12
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    Ahhh! I get it! Thanks archer90, Moo and xifentoozlerix

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

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

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