Use this function to answer the following G(x) = 7 sin (5?/8...

Use this function to answer the following G(x) = 7 sin (5?/8 x + 9?/16) - 4 11. amplitude = 7 period = ___ translated origin = ( , ) 1/4 step if used = ___ 12. Sketch at least one period of G(x) on the axes below. Label key points/values.

Transcript

00:01 Hi, in this question we're given this function g of x, a sinusoidal function, and we want to answer some things about it.

00:08 So the first thing we want to say is what's the amplitude, and this is controlled simply by this number here, multiplied out front.

00:20 So we see that the amplitude is 7.

00:25 Then for the period, this is given by the coefficient of the x in the sine function, but then we divide it by 2 pi.

00:34 So it's going to be 5 pi over 8, divided by 2 pi, so that's 5 over 16.

00:43 And then we want the translated origin, so usually the origin is 0 ,0, but now we want to see sort of where this starts.

00:56 So the first thing we have to do is to solve 5 pi over 8 x plus 9 pi over 16 equals 0.

01:06 So this gives us x equals negative 9 pi over 16 over 5 pi over 8.

01:16 So the pi's cancel, we get negative 9 over 5 times 8 over 16, so that's 1 over 2, so we get negative 9 over 10.

01:30 And then the y value is going to be translated by minus 4.

01:34 So the translated origin is going to be negative 9 over 10, comma, negative 4.

01:40 And then finally we want to sketch one period of this.

01:50 So let's do something like this.

01:54 So it's sort of centered at negative 4, and then it has a period of amplitude of 7, so it's going to go down to minus 11.

02:03 So that's like here, and then up to 3.

02:09 And then at negative 9 over 10, it's going to sort of start here.

02:18 Hi...

Question

Use this function to answer the following G(x) = 7 sin (5?/8 x + 9?/16) - 4 11. amplitude = 7 period = _ translated origin = ( , ) 1/4 step if used = _ 12. Sketch at least one period of G(x) on the axes below. Label key points/values.

Question

Use this function to answer the following G(x) = 7 sin (5?/8 x + 9?/16) - 4 11. amplitude = 7 period = ___ translated origin = ( , ) 1/4 step if used = ___ 12. Sketch at least one period of G(x) on the axes below. Label key points/values.

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Use this function to answer the following G(x) = 7 sin (5?/8 x + 9?/16) - 4 11. amplitude = 7 period = _ translated origin = ( , ) 1/4 step if used = _ 12. Sketch at least one period of G(x) on the axes below. Label key points/values.