Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle

Question

Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle

Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle `45^0` and its slope becomes `3.` Find the angle `thetadot`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Originally,the slope of the line is `tan theta=m`.
Nowm, the slope of the line after rotation is 3.
Angle between the old position and the new position of lines is `45^@`. Therefore, we have
`tan45^@=(3-m)/(1+3m)`
or ` 1+3m=3-m`
or `4m=2`
or `m=(1)/(2)=tantheta`
or `theta=tan^(-1)(1/2)`

11 views Answered 2023-02-05 15:29