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Sin & Cos with Amplitude and Phase.
Trigonometric equations are applied in the world of TV / cable broadcast. Equations such as y=2 sin ๐ฅ is an example of such an equation.
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Sin & Cos with Amplitude and Phase.
Trigonometric equations are applied in the world of TV / cable broadcast. Equations such as y=2 sin ๐ฅ is an example of such an equation. In the equation, 2 is a multiplier and called an amplitude. Amplitude describes the โheightโ of the trigonometric function.
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Sin & Cos with Amplitude and Phase.
Trigonometric equations are applied in the world of TV / cable broadcast. Equations such as y=2 sin ๐ฅ is an example of such an equation. In the equation, 2 is a multiplier and called an amplitude. Amplitude describes the โheightโ of the trigonometric function. ๐ฆ=๐ด ๐ ๐๐ ๐ฅ Letโs compare to y=2 sin ๐ฅ on the interval [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ
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Sin & Cos with Amplitude and Phase.
Trigonometric equations are applied in the world of TV / cable broadcast. Equations such as y=2 sin ๐ฅ is an example of such an equation. In the equation, 2 is a multiplier and called an amplitude. Amplitude describes the โheightโ of the trigonometric function. ๐ฆ=๐ด ๐ ๐๐ ๐ฅ Letโs compare to y=2 sin ๐ฅ on the interval [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ ๐ฆ=๐ ๐๐ ๐ฅ 2 sin 0๐= sin ๐ 4 = 1 sin ๐ 2 = sin 3๐ 4 = sin ๐= ๐ 4 ๐ 2 3๐ 4 ๐ 5๐ 4 3๐ 2 7๐ 4 2๐ sin 5๐ 4 = -1 sin 3๐ 2 = sin 7๐ 4 = -2 sin 2๐=
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Sin & Cos with Amplitude and Phase. ๐ฆ=๐ด ๐ ๐๐ ๐ฅ
I used just basic angles and plotted my sin x curve. Letโs compare to y=2 sin ๐ฅ on the interval [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ ๐ฆ=๐ ๐๐ ๐ฅ 2 sin 0๐= 0 sin ๐ 4 =0.7071 1 sin ๐ 2 = 1 5๐ 4 7๐ 4 sin 3๐ 4 =0.7071 sin ๐=0 ๐ 4 ๐ 2 3๐ 4 ๐ 3๐ 2 2๐ sin 5๐ 4 =โ0.7071 -1 sin 3๐ 2 =โ1 sin 7๐ 4 =โ0.7071 -2 sin 2๐=0
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Sin & Cos with Amplitude and Phase. ๐ฆ=๐ด ๐ ๐๐ ๐ฅ
I used just basic angles and plotted my sin x curve. Now letโs get our values for y=2 sin ๐ฅ Letโs compare to y=2 sin ๐ฅ on the interval [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ ๐ฆ=๐ ๐๐ ๐ฅ y=2 sin ๐ฅ 2 sin 0๐= 0 2 sin 0๐= sin ๐ 4 =0.7071 2 sin ๐ 4 = 1 sin ๐ 2 = 1 2 sin ๐ 2 = 5๐ 4 7๐ 4 sin 3๐ 4 =0.7071 2 sin 3๐ 4 = sin ๐=0 2 sin ๐= ๐ 4 ๐ 2 3๐ 4 ๐ 3๐ 2 2๐ sin 5๐ 4 =โ0.7071 2 sin 5๐ 4 = -1 sin 3๐ 2 =โ1 2 sin 3๐ 2 = sin 7๐ 4 =โ0.7071 2 sin 7๐ 4 = -2 sin 2๐=0 2 sin 2๐=
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Sin & Cos with Amplitude and Phase. ๐ฆ=๐ด ๐ ๐๐ ๐ฅ
I used just basic angles and plotted my sin x curve. Now letโs get our values for y=2 sin ๐ฅ As you can see, all the values doubled ( x 2 ) Letโs compare to y=2 sin ๐ฅ on the interval [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ ๐ฆ=๐ ๐๐ ๐ฅ y=2 sin ๐ฅ 2 sin 0๐= 0 2 sin 0๐=0 sin ๐ 4 =0.7071 2 sin ๐ 4 =1.414 1 sin ๐ 2 = 1 2 sin ๐ 2 =2 5๐ 4 7๐ 4 sin 3๐ 4 =0.7071 2 sin 3๐ 4 =1.414 sin ๐=0 2 sin ๐= 0 ๐ 4 ๐ 2 3๐ 4 ๐ 3๐ 2 2๐ sin 5๐ 4 =โ0.7071 2 sin 5๐ 4 =โ1.414 -1 sin 3๐ 2 =โ1 2 sin 3๐ 2 =โ1 sin 7๐ 4 =โ0.7071 2 sin 7๐ 4 = โ1.414 -2 sin 2๐=0 2 sin 2๐= 0
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Sin & Cos with Amplitude and Phase.
Phase relation is seen in practical applications such as sound, electrical, and radio waves. This โphase shiftโ adjusts the wave by sliding it either left or right a number of degrees. The waves mostly frequently shifted are sine waves. ๐ฆ=๐ ๐๐ ๐ฅยฑโ
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Sin & Cos with Amplitude and Phase.
Phase relation is seen in practical applications such as sound, electrical, and radio waves. This โphase shiftโ adjusts the wave by sliding it either left or right a number of degrees. The waves mostly frequently shifted are sine waves. ๐ฆ=๐ ๐๐ ๐ฅยฑโ
Here is an example of a sine wave shifted 45โฐ.
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Sin & Cos with Amplitude and Phase.
Phase relation is seen in practical applications such as sound, electrical, and radio waves. This โphase shiftโ adjusts the wave by sliding it either left or right a number of degrees. The waves mostly frequently shifted are sine waves. ๐ฆ=๐ ๐๐ ๐ฅยฑโ
Here is an example of a sine wave shifted 45โฐ. ( the interval is [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ sin 0๐= 0 1 sin ๐ 4 =0.7071 sin ๐ 2 = 1 5๐ 4 7๐ 4 sin 3๐ 4 =0.7071 sin ๐=0 ๐ 4 ๐ 2 3๐ 4 ๐ 3๐ 2 2๐ sin 5๐ 4 =โ0.7071 -1 sin 3๐ 2 =โ1 sin 7๐ 4 =โ0.7071 sin 2๐=0
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Sin & Cos with Amplitude and Phase.
Phase relation is seen in practical applications such as sound, electrical, and radio waves. This โphase shiftโ adjusts the wave by sliding it either left or right a number of degrees. The waves mostly frequently shifted are sine waves. ๐ฆ=๐ ๐๐ ๐ฅยฑโ
Here is an example of a sine wave shifted 45โฐ. ( the interval is [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ ๐ฆ=๐ ๐๐ ๐ฅ+45ยฐ sin 0๐= 0 sin 0+45ยฐ =0.7071 1 sin ๐ 4 =0.7071 sin ๐ 4 +45ยฐ =1 sin ๐ 2 = 1 5๐ 4 7๐ 4 sin 3๐ 4 =0.7071 sin ๐ 2 +45ยฐ =0.7071 sin ๐=0 ๐ 4 ๐ 2 3๐ 4 ๐ 3๐ 2 2๐ sin 5๐ 4 =โ0.7071 sin 3๐ 4 +45ยฐ =0 -1 sin 3๐ 2 =โ1 sin 7๐ 4 =โ0.7071 โฎ sin 2๐=0 And so on
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Sin & Cos with Amplitude and Phase.
Phase relation is seen in practical applications such as sound, electrical, and radio waves. This โphase shiftโ adjusts the wave by sliding it either left or right a number of degrees. The waves mostly frequently shifted are sine waves. As you can see, we either add or subtract the angle. ๐ฆ=๐ ๐๐ ๐ฅยฑโ
Here is an example of a sine wave shifted 45โฐ. ( the interval is [ 0 , 2ฯ ] ๐ฆ=๐ ๐๐ ๐ฅ ๐ฆ=๐ ๐๐ ๐ฅ+45ยฐ sin 0๐= 0 sin 0+45ยฐ =0.7071 1 sin ๐ 4 =0.7071 sin ๐ 4 +45ยฐ =1 sin ๐ 2 = 1 5๐ 4 7๐ 4 sin 3๐ 4 =0.7071 sin ๐ 2 +45ยฐ =0.7071 sin ๐=0 ๐ 4 ๐ 2 3๐ 4 ๐ 3๐ 2 2๐ sin 5๐ 4 =โ0.7071 sin 3๐ 4 +45ยฐ =0 -1 sin 3๐ 2 =โ1 sin 7๐ 4 =โ0.7071 โฎ sin 2๐=0 And so on
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