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Math Help - Exact values.

  1. #1
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    Exact values.

    1.Find the following exact trig values:
    sin210
    tan300
    cos270
    cos(-60)
    tan450
    sin240

    2.Name 2 angles with the value sinX=1

    ASAP please!
    THANKS
    Last edited by mr fantastic; April 28th 2010 at 07:44 PM. Reason: Re-titled.
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  2. #2
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    Hey,

    The unit circle will help you answer those.


    cos(degree) is the x value
    sin(degree) is the y value

    so cos(270) = 0.

    Does that make sense?
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  3. #3
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    Assuming trigonometric arguments in degrees
    1. -1/2
    2. -sqrt3
    3. 0
    4. 1/2
    5. complex infinity
    6. (-sqrt3)/2

    Assuming trigonometric arguments in radians
    1. 0.46771...
    or (I/2)/E^(210 I) - (I/2) E^(210 I)
    2. 45.2447...
    or (I (E^(-300 I) - E^(300 I)))/(E^(-300 I) + E^(300 I))
    3. 0.98438...
    or 1/(2 E^(270 I)) + E^(270 I)/2
    4. -0.9524...
    or 1/(2 E^(60 I)) + E^(60 I)/2
    5. 0.935809...
    or (I (E^(-450 I) - E^(450 I)))/(E^(-450 I) + E^(450 I))
    6. 0.945445...
    or (I/2)/E^(240 I) - (I/2) E^(240 I)

    For more alternate forms, width/height triangles when using sin, cos, tan, properties, decimal approximations, or alternate/integral representations, go to wolframalpha.com that can solve all if not most equations, even for x. remember technology is your friend!
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  4. #4
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    Thanks so much

    What would be the answer to "Name 2 angles with the value sin X=1"
    Also, is there a way to sketch triangles here?
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  5. #5
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    Quote Originally Posted by iluvmath101 View Post
    What would be the answer to "Name 2 angles with the value sin X=1"
    Also, is there a way to sketch triangles here?
    absolutely. Just go to that site like I said, and it makes one for you with height and length.

    as for sinx=1

    sin X=1 - Wolfram|Alpha

    there ya go!
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  6. #6
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    Quote Originally Posted by BrendanLoftus View Post
    absolutely. Just go to that site like I said, and it makes one for you with height and length.

    as for sinx=1

    sin X=1 - Wolfram|Alpha

    there ya go!
    Thanks for your help... Will it sound really stupid if I said I don't know what I'm looking at? I haven't been in math class for 2 weeks (sick) and I have a few questions I need to hand in tomorrow... Can you please just tell me what to write on my paper?
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  7. #7
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    for what part?
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  8. #8
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    Name 2 angles with the value sin X=1
    I have a few more questions if your up to it...
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  9. #9
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    Quote Originally Posted by iluvmath101 View Post
    Name 2 angles with the value sin X=1
    I have a few more questions if your up to it...
    These are values to be memorized, using the unit circle.
    You could use your calculator, 2nd function, then sine, then 1,then =. But,
    sin 90 =1
    cos 0 =1
    tan 45 =1

    In the unit circle, sine is 1at pi/2 (and all variations of it b y adding 2pi). So, when sin x = 1, x= pi/2 +2kpi where k is a constant.

    Similarly, cos x = 1 at angle 0, 2pi, etc. 2pi + 2kpi for short.

    Tanget is sin x / cos x. Therefore, tan x = 1 when sin x / cos x are equal (but different of 0).

    heres another way of looking at it

    on your calculator if you push second and then sin and then type in one it will give you the answer

    it works the same way for cosine and tan


    another way of thinking of it is that at what degree or radian will you get one

    at ninety degrees or 1/2 pi the sin will be one

    the cosine of 0 degrees, 360 degrees, 0pi, or 2pi will give you 1

    the tan of 45 degrees, 1/4pi, 225 degrees, and 5/4 pi will all give you one
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  10. #10
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    therefore; the two angels are 90 and -270
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  11. #11
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    Your a life saver

    Quote Originally Posted by BrendanLoftus View Post
    These are values to be memorized, using the unit circle.
    You could use your calculator, 2nd function, then sine, then 1,then =. But,
    sin 90 =1
    cos 0 =1
    tan 45 =1

    In the unit circle, sine is 1at pi/2 (and all variations of it b y adding 2pi). So, when sin x = 1, x= pi/2 +2kpi where k is a constant.

    Similarly, cos x = 1 at angle 0, 2pi, etc. 2pi + 2kpi for short.

    Tanget is sin x / cos x. Therefore, tan x = 1 when sin x / cos x are equal (but different of 0).

    heres another way of looking at it

    on your calculator if you push second and then sin and then type in one it will give you the answer

    it works the same way for cosine and tan


    another way of thinking of it is that at what degree or radian will you get one

    at ninety degrees or 1/2 pi the sin will be one

    the cosine of 0 degrees, 360 degrees, 0pi, or 2pi will give you 1

    the tan of 45 degrees, 1/4pi, 225 degrees, and 5/4 pi will all give you one
    thanks!
    Last edited by mr fantastic; April 28th 2010 at 07:47 PM. Reason: Deleted request to solve new questions tagged onto this thread.
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