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    given that sin(pi/3)=(root 3)/2 and cos (pi/3)=1/2 use trigonometric identities without the use of a calculator to determine the exact value of sin(2pi/3),cos(2pi/3), sin(5pi/6) and cos(5pi/6)

    can anyone help me with this please


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    Hint: \displaystyle \sin \left(\frac{2\pi}{3}\right)=\sin \left(\frac{\pi}{3}+\frac{\pi}{3  } \right) . Now use the identity for \displaystyle \sin(A+B) . You can do similar for the second one. Then for third and fourth use rewrite 5pi/6=pi-pi/6.
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    (Original post by poorform)
    Hint: \displaystyle \sin \left(\frac{2\pi}{3}\right)=\sin \left(\frac{\pi}{3}+\frac{\pi}{3  } \right) . Now use the identity for \displaystyle \sin(A+B) . You can do similar for the second one. Then for third and fourth use rewrite 5pi/6=pi-pi/6.

    You are an angel:littleangel:
    Thank you!

    I can't believe i forgot this.
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    how am i supposed to do sin(pi) and cos(pi) without a calculator?

    i know what they are but i need to roe i didnt use a calculator
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    (Original post by doctor_2_be)
    how am i supposed to do sin(pi) and cos(pi) without a calculator?

    i know what they are but i need to roe i didnt use a calculator
    Not quite sure what you're trying to say there!

    The values for sin(pi) and cos(pi) are quotable. Alternatively you can quote the values for sin(pi/2) and cos(pi/2) and then use the double angle formulae if you want to derive the answers you want.
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    (Original post by davros)
    Not quite sure what you're trying to say there!

    The values for sin(pi) and cos(pi) are quotable. Alternatively you can quote the values for sin(pi/2) and cos(pi/2) and then use the double angle formulae if you want to derive the answers you want.
    prove
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    (Original post by davros)
    Not quite sure what you're trying to say there!

    The values for sin(pi) and cos(pi) are quotable. Alternatively you can quote the values for sin(pi/2) and cos(pi/2) and then use the double angle formulae if you want to derive the answers you want.
    sorry should say show

    I decided to go with sin(pi/2) and showed it on the graph for both sin and cos
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    (Original post by doctor_2_be)
    You are an angel:littleangel:
    Thank you!

    I can't believe i forgot this.
    you are most welcome. don't forget to post in the maths study help not the university courses bit as you will get answers quicker.
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    (Original post by keromedic)
    prove
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     \text{Can you say that } \mathrm{sin(\pi) \equiv {cos}(\frac{\pi}{2})=0} \text{ or is this circular?}
    I'm not quite sure why you're using the identity symbol there, or how you're trying to relate the sine of pi to the cosine of pi/2!!

    I don't know what sort of course the OP is doing, but unless it's a University Analysis course then you should be able to quote sin(pi/2) = 1, cos(pi/2) = 0, sin(pi) = 0 and cos(pi) = -1 - these are just standard angles that you should know. There's no need to "derive" any of these results
 
 
 
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