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trigonometric identities HELP!!

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:s-smilie:


Thanks:smile:
Hint: sin⁡(2π3)=sin⁡(π3+π3)\displaystyle \sin \left(\frac{2\pi}{3}\right)=\sin \left(\frac{\pi}{3}+\frac{\pi}{3} \right) . Now use the identity for sin⁡(A+B)\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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doctor_2_be
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Original post by poorform
Hint: sin⁡(2π3)=sin⁡(π3+π3)\displaystyle \sin \left(\frac{2\pi}{3}\right)=\sin \left(\frac{\pi}{3}+\frac{\pi}{3} \right) . Now use the identity for sin⁡(A+B)\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.
Reply 3
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doctor_2_be
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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
(edited 8 years ago)
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davros
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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! :biggrin:

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.
Original post by davros
Not quite sure what you're trying to say there! :biggrin:

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
(edited 8 years ago)
Reply 6
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doctor_2_be
OP
3
Original post by davros
Not quite sure what you're trying to say there! :biggrin:

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:colondollar:

I decided to go with sin(pi/2) and showed it on the graph for both sin and cos
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.
Reply 8
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davros
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Original post by keromedic
prove

Spoiler



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 :smile:

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