{"version":9,"randomSeed":"c545e73c3fb63924ab2d571de690f53c","graph":{"viewport":{"xmin":-4.019262594433291,"ymin":-3.28621377394725,"xmax":4.5397734152763665,"ymax":3.0565757651913708}},"expressions":{"list":[{"type":"text","id":"42","text":"cis(theta) = cos(theta) + i * sin(theta) = e^(i * theta)"},{"type":"expression","id":"31","color":"#000000","latex":"B\\left(\\theta\\right)=\\left(\\cos\\theta,\\sin\\theta\\right)"},{"type":"text","id":"44","text":"cos in terms of cis"},{"type":"expression","id":"33","color":"#2d70b3","latex":"C\\left(\\theta\\right)=\\frac{B\\left(\\theta\\right)+B\\left(-\\theta\\right)}{2}"},{"type":"expression","id":"34","color":"#388c46","latex":"C\\left(x\\right).x"},{"type":"expression","id":"35","color":"#6042a6","latex":"C\\left(x\\right).y"},{"type":"expression","id":"40","color":"#6042a6","latex":"\\cos x"},{"type":"text","id":"46","text":"i * sin in terms of cis"},{"type":"expression","id":"36","color":"#000000","latex":"S\\left(\\theta\\right)=\\frac{B\\left(\\theta\\right)-B\\left(-\\theta\\right)}{2}"},{"type":"expression","id":"37","color":"#c74440","latex":"S\\left(x\\right).x"},{"type":"expression","id":"38","color":"#2d70b3","latex":"S\\left(x\\right).y"},{"type":"expression","id":"39","color":"#388c46","latex":"\\sin x"}]}}