Question

Sketch the graph of y = 5 sin 2x° + 12
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Answer 1

Function: y = 5 sin (2(x))+ 12

Find y-intercept:

y = 5 sin 2(0)+ 12

y = 12

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`\sf Y\:Intercepts}:\:\left(0,\:12\right)`

→ Formula for maximum: M = A + |B|

Maximum:

12 + |5|

17

When y = 17

`\rightarrow \sf 17 = 5 sin (2(x))+ 12`

`\rightarrow \sf \sf 5 sin (2(x)) = 5`

`\rightarrow \sf sin (2(x)) = 1`

`\rightarrow \sf 2x = sin^(-1)(1)`

`\rightarrow \sf 2x = 90^(\circ \:), \ \ 450^(\circ \:)`

`\rightarrow \sf x = 45^(\circ \:), \ \ 225^(\circ \:)`

maximum: ( 45° , 17 ), (225° , 17), .....

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→ Formula for minimum: m = A ‐ |B|

Minimum:

12 - |5|

7

When y = 7

`\rightarrow \sf 7 = 5 sin (2(x))+ 12`

`\rightarrow \sf 5 sin (2(x)) = -5`

`\rightarrow \sf 2(x) = sin^(-1)(-1)`

`\rightarrow \sf x = -45^(\circ \:) , \ \ 135^(\circ \:)`

minimum: ( -45°,7), (135°, 7), .....

Repeat the same process for finding more values on the x-axis, or just follow the trend of the curve from the points found and sketch the graph easily.

`\sf Domain\:\left(-\infty \: < x < \infty )`

`\sf Range : 7\le \:f\left(x\right)\le \:17`

Sketched below: