Question

Identify the correct equation that describe the relationship between a sine and cosine wave. a. v(t) = A sin (2πft + π/2) = A cos (2πft) b. v(t) = A sin (2πft) = A cos (2πft + π/2) c. v(t) = A sin (2πft ) = A cos (2πft) d. v(t) = A sin (2πft - π/2) = A cos (2πft)

Answer 1

Answer:

A. v(t) = sin (2πft + π/2) = A cos (2πft)

Step-by-step explanation:

According to trigonometry friction, the following relationship are true;

Sin(A+B) = sinAcosB + cosAsinB

We will be using this relationship to check which option is true.

Wave equation is represented as shown;

y(t) = Asin(2πft±theta)

For positive displacement,

y(t) = Asin(2πft+theta)

If theta = π/2

y(t) = Asin(2πft+π/2)

y(t) = A[ sin 2πftcosπ/2 + cos2πft sin π/2]

Since sinπ/2 = 1 and cos (π/2) = 0

y(t) = A[ sin 2πft (0)+ cos2πft (1)]

y(t) = A[0+ cos2πft]

y(t) = Acos2πft

Hence the expression that is true is expressed as;

v(t) = Asin(2πft+π/2) = Acos2πft