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Prove ( 1 – cos ^2 x) (1 + cos^2 x) = 2sin^2 x – sin^4 x Replace ##( 1 – cos^2 x)## by ##sin^2 x## […]

A (segment) bisector is any segment line or ray that splits another segment into two congruent parts. For example in the picture if ##bar(DE)congbar(EB)## then ##bar(AC)## […]

Sum of interior angles of a hendecagon ##=1620^@## The real issue here is knowing that a hendecagon is an ##11## sided (and angled) polygon. The formula […]

##SA=3750cm^2## The volume of a cube is determined by the formula ##V=s^3## where ##s## is the measurement of each edge. Since cube has six square faces […]

The length of short leg##=6.928## ##30^o##-##60^o##-##90^o## is a special kind of right-triangle in which sides exist in ratio ##SL:LL:H = 1:sqrt(3):2## where ##SL=##Short Leg ##LL=##Long Leg […]

I found: ##tan(theta)=1## Consider the following diagram: We can see that the relationships between rectangular and are: ##r=sqrt(x^2+y^2)## ##theta=arctan(y/x)## and: ##x=rcos(theta)## ##y=rsin(theta)## Given our expression: ##y=x## […]

##sin(cos^(-1)(x)) = sqrt(1-x^2)## Let’s draw a right triangle with an angle of ##a = cos^(-1)(x)##. As we know ##cos(a) = x = x/1## we can label […]

##theta=(2n+1)pi/2## or ##theta=2npi+-(2pi)/3## where ##n## is an integer. ##cos2theta=costheta## or ##2cos^2theta-1=costheta## (using formula for ##cos2theta##) the above becomes ##2cos^2theta-costheta-1=0## Now using quadratic formula ##costheta=(-(-1)+-sqrt((-1)^2-4*2*(-1)))/(2*2)## or ##costheta=(1+-sqrt(1+8))/4=(1+-3)/4## […]

Express ##(25pi)/6## to degree measure then get the terminal side of the angle. ##(25pi)/6=(25cancelpi)/6(180^o/cancelpi)=750^o## ##750^o = 360^o + 360^o + 30^o## that means there are 2 […]