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  1. #1
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    fraction

    How do I write 30 ˚ and 45 ˚ with fraction?
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  2. #2
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    Quote Originally Posted by kapital View Post
    How do I write 30 ˚ and 45 ˚ with fraction?
    Perhaps you mean how to write each angle in radians ....?
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  3. #3
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    I mean how i write 30˚ with number. For example sin90˚=1, cos180=-1,.....
    How is sin30˚, or sin˚45˚?(I dont know this, because i cant see thas, so i mus probably calculate anddont know how)
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  4. #4
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    Quote Originally Posted by kapital View Post
    I mean how i write 30˚ with number. For example sin90˚=1, cos180=-1,.....
    How is sin30˚, or sin˚45˚?(I dont know this, because i cant see thas, so i mus probably calculate anddont know how)
    You understand, don't you, that your initial post said nothing about sine and cosine?

    For 45 degrees think of an isosceles right triangle. If the two sides are both of length 1, then, by The Pythagoream theorem, the hypotenuse has length \sqrt{2}. So sin(45)= cos(45)= \frac{1}{\sqrt{2}}= \frac{\sqrt{2}}{2}.

    For 30 or 60 degrees, start with an equilateral triangle, with sides of length 1. Drop a perpendicular from one vertex to the opposite side. Since an equilateral triangle has angles of measure 60 degrees, this divides the triangle into two right triangles with angles of 30 and 60 degrees. The hypotenuse of the right triangles is 1 and the leg opposite the 30 degree angle is 1/2 that side of the equilateral triangle and so has length 1/2. By the Pythagorean theorem again, the other leg has length \sqrt{1- (1/2)^2}= \frac{\sqrt{3}}{2}.

    Thus, sin(30)= \frac{\frac{1}{2}}{1}= \frac{1}{2}. cos(30)= \frac{\frac{\sqrt{3}}{2}}{1}= \sqrt{3}{2}, sin(60)= \frac{\frac{\sqrt{3}}{2}}{1}= \sqrt{3}{2}, and cos(60)== \frac{\frac{1}{2}}{1}= \frac{1}{2}.
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  5. #5
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    Quote Originally Posted by kapital View Post
    I mean how i write 30˚ with number. For example sin90˚=1, cos180=-1,.....
    How is sin30˚, or sin˚45˚?(I dont know this, because i cant see thas, so i mus probably calculate anddont know how)
    In a right triangle:

     <br />
\sin A = \dfrac{ \text{opposite}} {\text{hypotenuse}}<br />

     <br />
\sin (30deg) = 0.5 = \dfrac{ 1 } { 2 }<br />

     <br />
\sin (45deg) = 0.707106781 = \dfrac{ 1 } { \sqrt{ 2 } }<br />

    also
     <br />
\cos A = \dfrac{ \text{adjacent}} {\text{hypotenuse}}<br />

    Is that what you are seeking?
    .
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  6. #6
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    Quote Originally Posted by HallsofIvy
    You understand, don't you, that your initial post said nothing about sine and cosine?
    Well, i had so many probles, with english, that i forget.



    What I am asking is how can I calulate the value of any cos and sin.

    When there is cos180, for example, i look here(http://www.cartage.org.lb/en/themes/...unitcircle.gif) and i can see that this is minus one. But i dont know how to calculate the values of 15,70,120,150,.... . When the value is diffrent than 90,180,270, i dont know how to calulate the value of sinus and cosinus.

    And soory again for my bad english.
    Last edited by mr fantastic; October 28th 2009 at 07:48 PM. Reason: Added quote tags.
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  7. #7
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    Quote Originally Posted by kapital View Post
    Well, i had so many probles, with english, that i forget.



    What I am asking is how can I calulate the value of any cos and sin.

    When there is cos180, for example, i look here(http://www.cartage.org.lb/en/themes/...unitcircle.gif) and i can see that this is minus one. But i dont know how to calculate the values of 15,70,120,150,.... . When the value is diffrent than 90,180,270, i dont know how to calulate the value of sinus and cosinus.

    And soory again for my bad english.
    In those cases you have to use double ange and compound angle formulas together with the known exact values already discussed. eg. \sin 15^0 = \sin (45^0 - 30^0) = .....
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  8. #8
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    But for general angles, "When the value is diffrent than 90,180,270, i dont know how to calulate the value of sinus and cosinus", the only thing to do is use a calculator! The ones I gave, 30, 45, and 60, your 90, 180, 27, and angles that, as Mr Fantastic says, can be reduced to those, are the only angles for which exact values of sine and cosine can be calculated.
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  9. #9
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    I have problem again and I can help with calculator, because the exercise says calculate EXACLLY:

    sin150˚
    cos225˚žsin210˚
    sin954˚
    sin 13pi/6
    cos(-7pi/4)

    thax and i hope somebody coud help.
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