Expert: Paul Klarreich - 2/26/2008

Question
Hi this is my second question.  It says: "Use the appropriate formula to find the exact value of the following expression:  sin(4pi/3 + pi/4)"  Thank you again

Answer
Questioner:   Rich
Category:  Advanced Math
Private:  No
 
Subject:  Formula Expression
Question:  Hi this is my second question.  It says: "Use the appropriate formula to find the exact value of the following expression:  sin(4pi/3 + pi/4)"  Thank you again
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HI, Rich,

In sin(4pi/3 + pi/4), your argument: 4pi/3 + pi/4, looks like a sum of two angles.  So your "appropriate formula" is the sine of the sum of two angles.

sin(A + B) = sin A cos B + cos A sin B.

and you take  A = 4pi/3,  B = pi/4.

sin(4pi/3 + pi/4) = sin 4pi/3 cos pi/4 + cos 4pi/3 sin pi/4

THEN, you use your knowledge of the 'special' triangles -- the 30-60 and 45-45 right triangles, and the signs in the quadrants, to get:

sin 4pi/3 = - sqrt(3)/2
cos pi/4 = sin pi/4 = sqrt(2)/2
cos 4pi/3 = - 1/2

and just plug them in.