1. Problem: Find the coordinates of the point $E(t)$ on the unit circle and determine the sine and cosine values for $t = \frac{321\pi}{2}$ (part a) and $t = \frac{141\pi}{2}$ (part f) from Zadaci 3.3.1. 2. Formula and rules: On the unit circle, the coordinates of $E(t)$ are $(\cos t, \sin t)$. Since the circle has period $2\pi$, angles differing by multiples of $2\pi$ correspond to the same point. 3. Calculate $t$ modulo $2\pi$: - For $t = \frac{321\pi}{2}$: $$\frac{321\pi}{2} = 321 \times \frac{\pi}{2}$$ Since $2\pi = \frac{4\pi}{2}$, find remainder when 321 is divided by 4: $$321 \div 4 = 80 \text{ remainder } 1$$ So, $$t \equiv \frac{1\pi}{2} = \frac{\pi}{2} \pmod{2\pi}$$ Therefore, $$\cos \frac{321\pi}{2} = \cos \frac{\pi}{2} = 0$$ $$\sin \frac{321\pi}{2} = \sin \frac{\pi}{2} = 1$$ - For $t = \frac{141\pi}{2}$: $$141 \div 4 = 35 \text{ remainder } 1$$ So, $$t \equiv \frac{\pi}{2} \pmod{2\pi}$$ Hence, $$\cos \frac{141\pi}{2} = 0$$ $$\sin \frac{141\pi}{2} = 1$$ 4. Explanation: Because the unit circle repeats every $2\pi$, we reduce the angle modulo $2\pi$ to find the equivalent angle in the first rotation. Both $\frac{321\pi}{2}$ and $\frac{141\pi}{2}$ reduce to $\frac{\pi}{2}$, where cosine is 0 and sine is 1. Final answers: - For $t = \frac{321\pi}{2}$: $\cos t = 0$, $\sin t = 1$ - For $t = \frac{141\pi}{2}$: $\cos t = 0$, $\sin t = 1$