SOLUTION: Please can you tell me why do these angles equal to the same? Why do these patterns occur? Sin 10`= Cos 90` , Sin20`=cos80`,sin90`/cos90`=tan 90 both of which is an error? Also

Question 960177: Please can you tell me why do these angles equal to the same? Why do these patterns occur? Sin 10`= Cos 90` , Sin20`=cos80`,sin90`/cos90`=tan 90 both of which is an error?
Also why does sin^2(10)+cos^2(10)=1,sin^2(23)+cos^2(23)=1,sin^2(35)+cos^2(35)=1
Can you explain why all the answers equals to 1?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Your reference angles are not correct.

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or in general in the first quadrant (0

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The angles and corresponding reference angles have the property that the points they represent are reflected about the line which has the property that swap x and y coordinates.
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It does so because,

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.

So,

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