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Its typically helpful to start with a drawing. Here is ##ABCD## as given by the problem. We are looking for the length of the shorter diagonal […]

##sin90^@ = 1## and ##sin135^@ = sqrt2/2## Therefore ##sin90^2 + sin135^@ = 1+sqrt2/2 = (2+sqrt2)/2##

To convert from polar to rectangular: ##x=rcos theta ## ##y=rsin theta## To convert from rectangular to polar: ##r^2=x^2+y^2## ##tan theta= y/x## This is where these equations […]

From the basic definitions of ##sin## and ##cos## and ##cos^2(x)+sin^2(x) = 1## or ##cos^2(x) = 1 -sin^2(x)## So ##cos^2(x) – sin^2(x)## ##= (1-sin^2(x))-sin^2(x)## ##= 1-2sin^2(x)##

This formula can be simplified to ##-sin60=-sqrt(3)/2## ##sin20cos80-cos20sin80=sin(20-80)=sin(-60)=-sin60=-sqrt(3)/2##

Area ##= 2sqrt(2)r^2## where ##r## is the radius of the octagon Consider the diagram below with radius ##r##: A regular octagon can be thought of as […]

##28 pi## or approximately 87.9646 By definition the lateral area of a cone is… ##A_l = L * pi * r## where ##L## is the slant […]

the polygon is *heptagon (7-sided polygon) Sum of interior angles is ##180(n-2)## Since sum is ##=900## ##900=180(n-2)## ##900/180=(180(n-2))/180## ##900/180=(cancel180(n-2))/cancel180## ##5=n-2## ##5+2=n## ##7=n##

If ##csctheta=4/3## then ##sintheta =3/4## also ##sintheta=a/c## therefore ##a=3 c=4## using Pythagorean theorem ##b=sqrt7.## ##costheta = b/c=sqrt7/4## ##tantheta=3/sqrt7=(3sqrt7)/7## ##sectheta=c/b=4/sqrt7=(4sqrt7)/7## ##cottheta= b/a = sqrt7/3##