Use standard identities to express

AI Thread Summary
To express sin(x + π/3) in terms of sin x and cos x, the standard identity sin(a + b) is applied, resulting in the equation sin(x)cos(π/3) + sin(π/3)cos(x). This simplifies to 0.5sin(x) + 0.8660cos(x). It is suggested to use the exact value for sin(π/3) as √3/2 instead of the decimal approximation. The discussion confirms that the expression is correct and emphasizes using exact values for clarity. Overall, the solution is on the right track and does not require further simplification.
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Homework Statement


Use standard identities to express sin(x+pi/3) in terms of sin x and cos x


Homework Equations



sin(a+b)=sinAcosB+sinBcosA


The Attempt at a Solution



sin(x)cos(pi/3)+sin(pi/3)cos(x)
0.5sinx + 0.8660cosx

I'm just not sure if i need to simplify it even further and hopefully I'm on the right track. Thanks
 
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That should be fine. I would just express 0.866 as √3/2 as that is an exact value whilst 0.866 is just an approximation.
 
that seems right to me. However I'd keep sin(π/3) as \frac{\sqrt{3}}{2}.

Edit: I didn't see rock.freak667's reply.
 
thanks for the response :)
 
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