What is the exact value of sin 240º?

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The exact value of sin 240º can be determined by recognizing that 240º is in the third quadrant, where sine values are negative. It can be expressed as 240º = 180º + 60º, allowing the use of the sine of 60º, which is √3/2. Since sine is negative in the third quadrant, the value of sin 240º is -√3/2. This confirms the calculation and understanding of the sine function in relation to angle quadrants.
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Homework Statement


Find the exact value of each trig function:
Sin 240º


Homework Equations





The Attempt at a Solution


I am so lost here. I have no attempt. I am not asking you for the answer (i can't get answer without making an attempt which I don't have) i just need help. Please.
 
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Try to express 240 as sum or difference of angles for which you know the value of sinӨ like 360, 30, 60 etc.
 
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so 240 is 60 degrees more than the 180 line of quadrant 2 so sin 60 = √3/2. is that right or am i totally off?
 
Corkery said:
so 240 is 60 degrees more than the 180 line of quadrant 2 so sin 60 = √3/2. is that right or am i totally off?
sin is -ve in 3rd and 4th quadrant
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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