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What is the value of Sin345?
Asked by Rajendra Prasad Por Last Modified
Answer 
Sin(345)=sin(360+(-15))=sin(-15)=-sin(15)
=-Sin(45-30)
Sin(A-B)=sinA cos(B) - cos(A)sin(B)
=-Sin(15)=-sin(45-30)
=-[Sin(45)cos(30) -cos(45)sin(30)]
=-[(1/√2)(√3/2) - (1/√2)(1/2)]
=-[(√3 -1)/(2√2)]
=-[(1.732-1)/(2*1.414)]
=-[(0.732)/2.828]
=-0.2588
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Assuming we're in degrees, we have
sin(345) = sin(300 + 45)....and using sin(A + B) = sinAcosB + sinBcosA, we have
sin300cos45 + sin45cos300 =
(-√3/2)(1/√2) + (1/√2)(1/2) =
-√3/ (2√2) + 1/(2√2) =
[ 1 - √3 ] / (2√2) and rationalizing the denominator, we have
√2 [ 1 - √3] / 4 =
(√2 - √6) / 4
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