Soh Cah Toa
Soh #->" sin = " ("opposite")/("hypotenuse")#
Cah #->"cos = "("adjacent")/("hypotenuses")#
Toa #-> "tan = "("opposite")/("adjacent")#
Given: #(sin(45^o))/(cos(30^o)+sin(60^o)) #
Note that #sin(45^o)=1/sqrt(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the #cos(30^o)+sin(60^o)#
Looking at the diagram we have
#cos(30^o)+sin(60^o)=(sqrt(3 ))/2+(sqrt(3 ))/2 = sqrt(3 )#
so #1/(cos(30^o)+sin(60^o))=1/sqrt(3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all together we have:
#1/sqrt(2)xx1/(sqrt(3))color(white)("d") -> color(white)("d")1/(sqrt(2)sqrt(3))#
#color(white)("dddddddddd")->color(white)("d")1/(sqrt(6))#
It is considered bad mathematical practice to have a root as or in the denominator if avoidable
Multiply by 1 and you do not change the value. However, one comes in many forms.
#color(white)("dddddddddd")->color(white)("d")1/(sqrt(6))xx1#
#color(white)("dddddddddd")->color(white)("d")1/(sqrt(6))xx(sqrt6)/(sqrt6)#
#color(white)("dddddddddd")->color(white)("d")(sqrt(6))/6#
