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Thread: Trigonometry

  1. #1 Trigonometry 
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    I hate to post this question here but I really can't seem to solve it.

    Find the value of x without plotting the graph,
    sin x + cos x = tan x

    I tried EVERYTHING! maybe I am not seeing something... Can anyone please help me out..

    This is not a homework question.... 16 year olds in Malaysia do not receive such difficult questions... Well questions like (sin x + cos x = 1) is considered difficult so... yeah...

    pardon me for the impertinence


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  3. #2  
    Forum Professor river_rat's Avatar
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    I doubt that equation has nice, easily accessible solutions. Where did you get it from?


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  4. #3  
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    Lol... while i was sitting for an math exam... I finished early and was very very bored.. so I came up with the question 3sin x + 2 kos x = 3 and challenged my friends to do it...

    This very good friend of mine called me to tell me the answer (not knowing that i've already found it), obliged to enlighten me.. However, when I told him i've already found the answer, he was rather disappointed.. Hence i wanted to come up with another hard question, and pretend not to know the answer this time..

    I came up with sin x + cos x = tan x..... Much to my own surprise.. I couldn't solve it myself..... 8)
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  5. #4  
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    sin x + cos x = tan x

    This looks solvable, but I doubt if the result would be "interesting".

    Let t = tan x/2

    Then sin x = 2t/(1+t^2), cos x = (1-t^2)/(1+t^2), tan x = 2t/(1-t^2)

    Substitute and cross multiply, this will give you an quartic equation in t.

    That can be solved by the standard method (see Google...)

    I don't have the patience to actually work out the details though.
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  6. #5 No solution? 
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    I think the question has no solution.

    Consider the following, angles in degrees

    sin x + cos x = tan x

    sin (90-x) + cos (90-x) = tan (90-x)

    Hence

    tan x = tan (90-x)

    Thus x = 45, which doesn't fit into the question.
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  7. #6 Re: No solution? 
    Forum Professor river_rat's Avatar
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    Quote Originally Posted by enoughsaid05
    I think the question has no solution.

    Consider the following, angles in degrees

    sin x + cos x = tan x

    sin (90-x) + cos (90-x) = tan (90-x)

    Hence

    tan x = tan (90-x)

    Thus x = 45, which doesn't fit into the question.
    Okay, you made a subtle mistake there (be careful repeating variables)

    The equation you actually get is that tan(x<sub>1</sub>) = tan(pi/2 - x<sub>2</sub>) which is a very different implication to the one you used.

    This equation has solutions btw, just not very nice ones.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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