Question

- Problem 6. Consider the function y2 m) sin ((10/s) t+π/4). lndicate whether each of the following waveforms is equivalent to y? Briefly justify your answers 1. (2 m) cos(10/s)t+/4) 2. (2 m) cos( (10/s)t+3 T/4) 3. (2m) cos( (10/s)t -/4) 4. (2 m) sin((10/ s) t + π/4 + 4 π) 5.-(2 m) sin ((10/s) t + π /4-3r) 6. (-2m) cos((10/s) t + 12n/4) 7. (v ฐ m) [cos((10/s) t) + sin((10/s) t)] 8. (2 m) cos ((-10/s) t +r/4) 9. (2 m) sin ( (-10 /s) t-π /4) 10. (./2 m) [-cos( (10/s) t ± π)-sin(( 10 /s) t-π)

Answer 1

1.

the angle is common for both but we have Cos which does not give the same waveform as "y"

not equivalent

2.

(2m) Cos((10) t + 3$\pi$/4)

(2m) Cos((10) t + $\pi$/4 + $\pi$/2)

- (2m) Sin((10) t + $\pi$/4 )

hence not equivalent

3.

(2m) Cos((10) t - 3$\pi$/4)

(2m) Cos((10) t - $\pi$/4 - $\pi$/2)

(2m) Cos(- (($\pi$/2) - ((10) t - $\pi$/4 ))

(2m) Sin((10) t - $\pi$/4 )

hence not equivalent

4.

(2m) Sin((10) t + $\pi$/4 + 4$\pi$)

(2m) Sin((10) t + $\pi$/4 )

hence equivalent

5.

- (2m) Sin(10 t + $\pi$/4 - 3 $\pi$)

- (2m) Sin(- (3 $\pi$ - (10 t + $\pi$/4) ))

(2m) Sin((3 $\pi$ - (10 t + $\pi$/4) ))

(2m) Sin(10 t + $\pi$/4) )

hence equivalent