Page 24 - Mathematics Class - XII

9. From the points A , A , A , A , A , A , A , A , A , A , A , A , draw perpendicular on the line y = x and
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produce these perpendiculars in equal length to the other side and fix the pins as B , B , B , B , B , B , B ,
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B , B , B , B , B .
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10. Join the pins with threads or rubber band to get the graph of sin x.
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11. Now, place a mirror on the line y = x. We see that image of graph of sin x in the mirror will represent graph
of sin x.
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DEMONSTRATION
Put a mirror on the line y = x. We see that image of graph of sin x in the mirror will represent graph of sin x and
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vice-versa.
OBSERVATION
Put a mirror on the line y = x. We noticed that the image of the graph of sin x in the mirror will represent the graph
of sin x.
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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The image of A in the line y = x i.e., the mirror is B .
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CONCLUSION
The mirror image of the graph of sin x about the line y = x is the graph of sin x, and the mirror image of graph of
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sin x about the line y = x is the graph of sin x.
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APPLICATION
Similar activity can be performed for drawing the graphs of cos x, tan x etc.
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Knowledge Booster
sin x should not be confused with (sin x) .
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In fact (sin x) =
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sin x
Which holds true for other trigonometric functions.

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