$Calculate Cosine Using Unit Circle in the Complex Plane$
Answer 1
Benjamin Clark
Consider a point on the unit circle in the complex plane, given by the complex number $z = e^{i\theta}$ where $\theta$ is the angle in radians from the positive x-axis.
The coordinate of this point can be written as $(\cos\theta, \sin\theta)$.
If $\theta = \frac{\pi}{4}$, find the cosine of $\theta$.
Since $\theta = \frac{\pi}{4}$, we can substitute into the formula:
$\cos\left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$
Answer 2
Ava Martin
Consider a point on the unit circle in the complex plane, given by the complex number $z = e^{i heta}$ where $ heta$ is the angle in radians from the positive x-axis.
The coordinate of this point can be written as $(cos heta, sin heta)$.
If $ heta = frac{pi}{6}$, find the cosine of $ heta$.
Since $ heta = frac{pi}{6}$, we can substitute into the formula:
$cosleft( frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
Answer 3
Emma Johnson
Consider a point on the unit circle in the complex plane, given by the complex number $z = e^{i heta}$ where $ heta$ is the angle in radians from the positive x-axis.
The coordinate of this point can be written as $(cos heta, sin heta)$.
If $ heta = frac{pi}{3}$, find the cosine of $ heta$.
Since $ heta = frac{pi}{3}$, we can substitute into the formula:
$cosleft( frac{pi}{3}
ight) = frac{1}{2}$
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