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Size:  8.3 KBall information in the picture thanks for you help!
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    (Original post by madfish)
    Name:  ws.png
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Size:  8.3 KBall information in the picture thanks for you help!
    Sketch a sin graph and you'll see
    Hint: sin(x) = 0
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    Hi madfish,

    You have two equations to solve from your question which you have correctly identified. sin(x)=0 and cos(x)=-sqrt(3)/2. We are, however, missing the interval for the results because there are an infinite number of solutions without one. What is the exact question?

    Let's start with sin(x). You should know what the curve looks like, but here



    So where on this is sin(x) 0?

    Now for the cos(x) graph:



    Notice how it's symmetrical in the Y-axis, meaning that cos(x)=cos(-x) so if you solve cos(x)=-sqrt(3)/2 and get an answer you also have the negative value of that as an answer.

    Tom
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    (Original post by tom982)
    Hi madfish,

    You have two equations to solve from your question which you have correctly identified. sin(x)=0 and cos(x)=-sqrt(3)/2. We are, however, missing the interval for the results because there are an infinite number of solutions without one. What is the exact question?

    Let's start with sin(x). You should know what the curve looks like, but here



    So where on this is sin(x) 0?

    Now for the cos(x) graph:



    Notice how it's symmetrical in the Y-axis, meaning that cos(x)=cos(-x) so if you solve cos(x)=-sqrt(3)/2 and get an answer you also have the negative value of that as an answer.

    Tom
    brilliant response tom, thank you

    but how do we get the 180?
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    how do we get the 180?

    thanks
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    (Original post by madfish)
    how do we get the 180?

    thanks
    By opening your eyes, and using the graphical answers people have given you.

    Sin(x)=0

    At 180, according the diagram people just posted. If you followed the curve back to the negative axis, you can see at -90, it'll be -1, and at -180 it'll be 0. Hence your +- 180 values.

    Now, Cos(x)=-root(3)/2 is 150. Look at the diagrams provided. Cos is symmetrical about the y axis, thus -150 is also the same.

    You could however recall that to gain other solutions, in the case of Sin(x) is 180-x, and for Cos(x) is 360-x.

    So infact, 360-150 is also a value, 210.

    As Cos(210) = -root(3)/2.

    And this therefore means due to symmetry that, -210 is also a value.
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    (Original post by madfish)
    how do we get the 180?

    thanks
    Again, looking at the sine curve:



    Since we are solving for sin(x)=0, we are looking for values of X when Y=0, so one way to look at this is to think where does this cross the X axis? There are infinitely many, as I previously said, but just tell me the ones in that image for teaching purposes.

    Tom
 
 
 
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