Question

Which of the following is not a right
way to express the sinusoid: A
cos(wt)
O A cos (2 rift)
O A cos(2 rt/T)
O A cos w(t-T)
O A sin(wt - 90°)​

Answer 1

Answer:

4 cos(2rift)

Explanation:

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Answer 2

(D) A Sin(ωt - 90°)

Explanation:

(A)EXPRESSION: A cos2πft.

Here, ω = 2πf ----(1)

let us verify the equation

A cosωt = A cos2πft

              = A cosωt

(B) EXPRESSION: A cos (2πt/T).

Here, f = 1/T

let us verify the equation

A cosωt = A cos( 2πt/T)

              = A cos(2πft)

              =A cosωt  ( from equation 1)

(C) EXPRESSION: A cosω(t-T)

As we know sine function is a periodic function, therefore, time shifting does not affect the expression. So, (t-T) = t

A cosωt = A cosω(t-T)

              = A cosωt

(D) EXPRESSION: A sin(ωt -90°)

We know that sin(Ф - 90°) = -cos(Ф)

Therefore, Sin(ωt - 90°) = -cos(ωt)

let us verify the equation,

A cosωt = A sin(ωt - 90°)

              ≠ -A cosωt

Therefore, in expression (D), L.H.S ≠ R.H.S

So, The answer is option (d) A sin(ωt - 90°)

There is some mistake in your question, but probably your correct question is:

Which of the following is not a right way to express the sinusoid A cos ωt?

(a) A cos 2π ft

(b) A cos (2πt/T)

(c) A cos ω(t - T)

(d) A sin (ωt - 90°)