Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Is this correct? The graphs of Sine and Cosine are positive in the first quadrant, but negative in the second, third, and fourth quadrants.?

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Thank you all who answered, I am very grateful!

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  • ?
    Lv 7
    2 months ago
    Favorite Answer

    All Silly Tom Cats...Q1 Q2 Q3 Q4

    i.e. sine, cosine and tangent are positive in Q1

    Only sine is positive in Q2

    Only tangent is positive in Q3

    Only cosine is positive in Q4

    This should help:

    https://www.onlinemathlearning.com/trig-equations-...

    :)>

  • Who
    Lv 7
    2 months ago

     nope- they are 90degrees out of phase

  • 2 months ago

    For determining Positivity / negativity of  the graph of trigonometrical ratios, there is a simple rule.  

    "sine is represented by y-axis, and cosine is represented by x-axis" 

    It means sin is positive if y axis is positive i.e. in First and Second Quadrants  and sin is negative in Third and Fourth Quadrants.  Similarly cos (ie x-axis) is  positive in First and Fourth quadrants, while cos (x-axis) is negative in Second and Third Quadrants.

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  • ?
    Lv 7
    2 months ago

    Take sin x. positive in first quadrant

    sin (x+pi/2)= sin x cos pi/2+ cos x sin pi/2=cos x= positive. Second quadrant.

    sin(x+pi)= sin x cos pi+ cos x sin pi= - sin x. Third quadrant

    sin (2 pi -x)= sin 2pi cos x- cos 2pi sin x=-sin x. Fourth quadrant. It is negative.

    cox is positive in first quadrant.

    cos (x+pi/2)= - sin x. Negative in second quadrant.

    cos (x+pi)= cos x cos pi= -cos x. negative in the third quadrant

    cos (2pi-x)= cos 2pi cos x= cos x. +ve in the fourth quadrant. 

  • ?
    Lv 7
    2 months ago

    Of Course, it's incorrect.  

     Cosine is the same as the x-coordinate on the unit circle 

    Sine is the same as the y-coordinate on the unit circle   

    so in Q1 

    (x is positive, y is positive ) 

    cosine is positive , sine is positive 

    in Q2  ,  

    (x is negative ,  y is positive) 

    cosine is negative , sine is positive 

    in Q3  

    (x is negative, y is negative ) 

    cosine is negative, sine is negative 

    in Q4 

    (x is positive, y is  negative ) 

    cosine is positive ,   sine is negative 

  • Anonymous
    2 months ago

    I don't believe that's correct.  It seems to me they're 90 degrees out-of-phase with each other, so one starts at the origin and climbs into the positive range while the other is at its lowest value, beginning a climb toward zero.  So they can't both always be positive or negative, together.  They're going to be opposite each other at a couple different points.

    (But it's been a long time, and maybe my memory is a bit fuzzy.)

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