Question4. Find the periods of a) $4+3 \sin \left(800 \pi t-15^{\circ}\right)$; b) $8,1 \cos ^{2} 9 \pi t$.
Ans. a) 2,5 ms; b) 111 ms .

Studdy Solution
Calculate the period of the function $\cos(18\pi t)$.
The period $T$ is given by:
$$T = \frac{2\pi}{|18\pi|} = \frac{2\pi}{18\pi} = \frac{1}{9}$$
Convert this period from seconds to milliseconds:
$$T = \frac{1}{9} \text{ seconds} = \frac{1}{9} \times 1000 \text{ ms} \approx 111.11 \text{ ms}$$
Rounding to the nearest millisecond gives $T = 111 \text{ ms}$.
The periods are $\boxed{2.5 \text{ ms}}$ for part (a) and $\boxed{111 \text{ ms}}$ for part (b).