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

Algebra ->  Trigonometry-basics -> 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       Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
Your reference angles are not correct.
sin%2810%29=cos%2880%29
sin%2820%29=cos%2870%29
.
.
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or in general in the first quadrant (0 sin%28X%29=cos%2890-X%29
cos%28X%29=sin%2890-X%29
.
.
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.
.
.
.
It does so because,
sin%5E2%28theta%29%2Bcos%5E2%28theta%29=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%5E2=%28x-0%29%5E2%2B%28y-0%29%5E2=1
x=cos%28theta%29
y=sin%28theta%29
So,
sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1