unit circle\ngiven $\frac{1}{2}=cos(\frac{pi t}{12})$, what is the value of $t$?\n$t =$

Explanation:

Step1: Recall cosine - value on unit - circle

We know that $\cos\theta=\frac{1}{2}$ when $\theta = 60^{\circ}$ or $\theta=\frac{\pi}{3}$ radians in the first - quadrant on the unit - circle.

Step2: Set up the equation

We are given $\frac{1}{2}=\cos(\frac{\pi t}{12})$, so $\frac{\pi t}{12}=\frac{\pi}{3}$.

Step3: Solve for t

Cross - multiply the equation $\frac{\pi t}{12}=\frac{\pi}{3}$. Multiply both sides by 12 to get $\pi t = 4\pi$. Then divide both sides by $\pi$. So $t = 4$.

Answer:

$4$