$ ext{Find the Trigonometric Values Using the Unit Circle}$

Given the angle $\theta = \frac{2\pi}{3}$, find the values of $\sin(\theta)$, $\cos(\theta)$, and $\tan(\theta)$ using the unit circle on a GDC TI calculator.

1. Locate the angle $\theta = \frac{2\pi}{3}$ on the unit circle.

2. The coordinates of the point where the terminal side intersects the unit circle are $(-\frac{1}{2}, \frac{\sqrt{3}}{2})$.

3. Hence, $\sin(\theta) = \frac{\sqrt{3}}{2}$, $\cos(\theta) = -\frac{1}{2}$, and $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} = \frac{\sqrt{3}}{2} \div -\frac{1}{2} = -\sqrt{3}$.

Therefore, the trigonometric values are:

$\sin(\frac{2\pi}{3}) = \frac{\sqrt{3}}{2}$

$\cos(\frac{2\pi}{3}) = -\frac{1}{2}$

$\tan(\frac{2\pi}{3}) = -\sqrt{3}$

Find the trigonometric values for the angle $ heta = frac{2pi}{3}$ on the unit circle using your GDC TI calculator.

1. Input the angle $frac{2pi}{3}$ into the calculator.

2. Use the unit circle to determine the coordinates: $(-frac{1}{2}, frac{sqrt{3}}{2})$.

3. Thus, $sin(frac{2pi}{3}) = frac{sqrt{3}}{2}$, $cos(frac{2pi}{3}) = -frac{1}{2}$, and $ an(frac{2pi}{3}) = frac{sin(frac{2pi}{3})}{cos(frac{2pi}{3})} = -sqrt{3}$.

Using your GDC TI calculator, find the trigonometric values for $ heta = frac{2pi}{3}$.

Coordinates: $(-frac{1}{2}, frac{sqrt{3}}{2})$

$sin(frac{2pi}{3}) = frac{sqrt{3}}{2}$

$cos(frac{2pi}{3}) = -frac{1}{2}$

$ an(frac{2pi}{3}) = -sqrt{3}$

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