Prove that the sum of the squares of the $sin$ and $cos$ functions on the unit circle equals 1.
Answer 1
Samuel Scott
On the unit circle, any point is represented as $(\cos(\theta), \sin(\theta))$, where $\theta$ is the angle formed with the positive x-axis.
According to the Pythagorean theorem, the equation of the unit circle is:
$ x^2 + y^2 = 1 $
Substituting the coordinates:
$ \cos^2(\theta) + \sin^2(\theta) = 1 $
Therefore, the sum of the squares of the sine and cosine functions on the unit circle equals 1.
Answer 2
Chloe Evans
The unit circle is defined by the equation:
$ x^2 + y^2 = 1 $
For any point on the unit circle at an angle $ heta$, the coordinates are given by:
$ x = cos( heta) $
$ y = sin( heta) $
Substituting these into the unit circle equation gives:
$ cos^2( heta) + sin^2( heta) = 1 $
Answer 3
Benjamin Clark
On the unit circle:
$ cos^2( heta) + sin^2( heta) = 1 $
Start Using PopAi Today