a.) sin(pi/12)= B.) sin(-pi/12)= C.) cos(11pi/8) d.) cos(-pi/12)= Solution a) si
ID: 2976527 • Letter: A
Question
a.) sin(pi/12)= B.) sin(-pi/12)= C.) cos(11pi/8) d.) cos(-pi/12)=Explanation / Answer
a) sin(15) = sin(45-30) sin45*cos30 - cos45*sin30 =>(1/?2)*(?3/2) - (1/?2)*(1/2) =>?3/2?2 - 1/2?2 =>(?3 - 1) /2?2 b)sin (-15) = - sin (15) = - ((sqrt 3) - 1) / 2 sqrt 2 = (1 - sqrt 3) / 2 sqrt 2 c)cos(247.5) = cos(180 + 67.5) = cos180 cos67.5 - sin180 sin67.5 = (-1) cos67.5 - (0) sin67.5 = -cos67.5 = -sin(90 - 67.5) = -sin22.5 = -?(2 - ?2) /2 d)cos 15 degrees = cos(45deg - 30deg) Use the difference identity cos(a - b) = (cosa)(cosb) + (sina)(sinb) = (1/sqrt2)(2/sqrt2) + (2/sqrt2)(sqrt3/2) = (2 + 2sqrt3)/2 = 1 + sqrt3
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