Question 960177
Your reference angles are not correct.
{{{sin(10)=cos(80)}}}
{{{sin(20)=cos(70)}}}
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or in general in the first quadrant (0<X<90),
{{{sin(X)=cos(90-X)}}}
{{{cos(X)=sin(90-X)}}}
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The angles and corresponding reference angles have the property that the points they represent are reflected about the line {{{y=x}}} which has the property that swap x and y coordinates.
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It does so because,
{{{sin^2(theta)+cos^2(theta)=1}}}
for any given x by definition.
The sine and cosine function are built off of a unit circle, a circle with a radius of 1 centered at (0,0). 
The cosine measures the x position on the circle.
The sine measures the y position on the circle.
The distance formula measures the distance from (x,y) to the center but since it's a circle the distance is always equal to the radius, 1.
{{{D^2=(x-0)^2+(y-0)^2=1}}}
{{{x=cos(theta)}}}
{{{y=sin(theta)}}}
So,
{{{sin^2(theta)+cos^2(theta)=1}}}