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Few questions i found confusing (Trigonometry & Graphs) Watch

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    I came across a few questions which i found a little confusing.

    A graph question which asked me to sketch the graphs
    2-|x+1| and 5-|x-1|
    and the asked me for the range
    I was confident that i had this right however the answer ended up with
    f(x)>2
    f(x)>5
    whereas i had
    f(x)≥2
    f(x)≥5
    I'm still not sure why the answer is right


    Trigonometry questions
    solving sin(x) -cos(x) = 0
    i first had done sin(x) +(sin^2 x -1)^(1/2) = 0
    however is this a correct approach to solving this sort of problem?
    (just wanted to know if there was any different standard procedures)

    proving that if A+B+C = 180
    then
    (tanA+tanB+tanC)/(tanAtanBtanC) = 1
    While i see that this works I'm not sure what you can do to prove it how do you go about proving it?

    Lastly a simple question that i can't seem to find information on in the book,maybe I'm interpreting the method wrongly..
    question:
    a) Express 3cos x - 4sin x in the form of R cos(x + a) i knew how to do this
    b) Find the greatest possible value of 2/(3cos x -4 sin x +6)
    My question with b is, what is the method you actually use to solve these sort of questions (greatest and minimum values), i can't see how b is related to part a other than the equation.

    Any help is very much appreciated
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    (Original post by Vanetti)
    I came across a few questions which i found a little confusing.

    A graph question which asked me to sketch the graphs
    2-|x+1| and 5-|x-1|
    and the asked me for the range
    I was confident that i had this right however the answer ended up with
    f(x)>2
    f(x)>5
    whereas i had
    f(x)≥2
    f(x)≥5
    I'm still not sure why the answer is right
    Provided that zero is in the domain of your function, then your answer is correct.

    Trigonometry questions
    solving sin(x) -cos(x) = 0
    i first had done sin(x) +(sin^2 x -1)^(1/2) = 0
    however is this a correct approach to solving this sort of problem?
    (just wanted to know if there was any different standard procedures)
    sin(x) - cos(x) = 0 implies that sin(x) = cos(x). Now divide both sides by cos(x); what do you get?

    proving that if A+B+C = 180
    then
    (tanA+tanB+tanC)/(tanAtanBtanC) = 1
    While i see that this works I'm not sure what you can do to prove it how do you go about proving it?
    Do you know the addition formula for tan(x+y)? Apply this twice to tan(A+B+C) - that is, do tan(A + (B+C)), then expand the tan(B+C).

    Lastly a simple question that i can't seem to find information on in the book,maybe I'm interpreting the method wrongly..
    question:
    a) Express 3cos x - 4sin x in the form of R cos(x + a) i knew how to do this
    b) Find the greatest possible value of 2/(3cos x -4 sin x +6)
    My question with b is, what is the method you actually use to solve these sort of questions (greatest and minimum values), i can't see how b is related to part a other than the equation.

    Any help is very much appreciated
    The greatest value of the expression you have there is achieved when the denominator is at its smallest. What is the smallest that 3cos x -4 sin x +6 can be? The connection with the first part is that the question I have posed is much easier to answer when you have the trig expression in the form R cos(x+a).
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    (Original post by Gregorius)
    Provided that zero is in the domain of your function, then your answer is correct.



    sin(x) - cos(x) = 0 implies that sin(x) = cos(x). Now divide both sides by cos(x); what do you get?



    Do you know the addition formula for tan(x+y)? Apply this twice to tan(A+B+C) - that is, do tan(A + (B+C)), then expand the tan(B+C).



    The greatest value of the expression you have there is achieved when the denominator is at its smallest. What is the smallest that 3cos x -4 sin x +6 can be? The connection with the first part is that the question I have posed is much easier to answer when you have the trig expression in the form R cos(x+a).
    Thank you so much everything makes perfect sense
 
 
 
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