Question

Find the magnitude of exp(jwt). find the boundness of sin(t) and cos(t).

a. 1, [-1,2], [-1,2]
b. 0.5, [-1,1], [-1,1]
c. 1, [-1,1], [-1,2]
d. 1, [-1,1], [-1,1]

Answer 1

The magnitude of exp(jwt) is 1, and the boundness of sin(t) and cos(t) both have the range [-1, 1]. Therefore, the correct answer is d. 1, [-1,1], [-1,1].

Step-by-step explanation:

The magnitude of exp(jwt) is 1 because the complex exponential function represents a point on the unit circle in the complex plane and thus has a constant magnitude of 1 regardless of the value of t or w.

The functions sin(t) and cos(t) are both bounded functions with a range of values from [-1, 1]. This is due to the trigonometric properties of sine and cosine functions, where they can only take values within this range on the unit circle.

Therefore, the correct answer to the question is d. 1, [-1,1], [-1,1].