Find the values of $sin$ and $cos$ for an angle on the unit circle
Answer 1
James Taylor
Given an angle $\theta$, find the values of $\sin(\theta)$ and $\cos(\theta)$ using the unit circle equation. Suppose $\theta = \frac{\pi}{4}$.
The unit circle equation is given by:
$x^2 + y^2 = 1$
For $\theta = \frac{\pi}{4}$, the corresponding point on the unit circle is $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.
Therefore,
$\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \quad \text{and} \quad \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}.$
Answer 2
Henry Green
Given an angle $ heta$, find the values of $sin( heta)$ and $cos( heta)$ using the unit circle equation. Suppose $ heta = frac{3pi}{2}$.
The unit circle equation is given by:
$x^2 + y^2 = 1$
For $ heta = frac{3pi}{2}$, the corresponding point on the unit circle is $left(0, -1
ight)$.
Therefore,
$sinleft(frac{3pi}{2}
ight) = -1 quad ext{and} quad cosleft(frac{3pi}{2}
ight) = 0.$
Answer 3
Daniel Carter
Given an angle $ heta$, find the values of $sin( heta)$ and $cos( heta)$ using the unit circle equation. Suppose $ heta = pi$.
The unit circle equation is given by:
$x^2 + y^2 = 1$
For $ heta = pi$, the corresponding point on the unit circle is $left(-1, 0
ight)$.
Therefore,
$sinleft(pi
ight) = 0 quad ext{and} quad cosleft(pi
ight) = -1.$
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