find the equation of straight line passes through a point (0 ,- 3 )which makes an angle tan^-1(1/3) with the line 3x- 2Y + 13 =0

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07-08-2021
Mathematics

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find the equation of straight line passes through a point (0 ,- 3 )which makes an angle tan^-1(1/3) with the line 3x- 2Y + 13 =0

Sagot :

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DWRead DWRead · Answer 1 · 2021-08-07T16:23:22-04:00

DWRead DWRead

07-08-2021

Answer:

Step-by-step explanation:

Edit:

y = (7/9)x = 3

Answer Link

sqdancefan sqdancefan · Answer 2 · 2021-08-07T20:17:24-04:00

9514 1404 393

Answer:

y = 11/3x -3

Step-by-step explanation:

The slope of a line is the tangent of the angle it makes with the x-axis. The slope of the given line is 3/2, so the angle it makes with the x-axis is arctan(3/2) ≈ 56.310°. We want a line that makes an angle of arctan(1/3) ≈ 18.435° with the given line, so its slope will be ...

tan(56.310° +18.435°) = tan(74.745°) = 11/3

The y-intercept of the desired line is given as (0, -3), so the equation of the line we want is ...

y = 11/3x -3

_____

Additional comment

The desired slope can be found using the formula for the tangent of the sum of angles. However, simply adding the angles on a calculator saves a lot of arithmetic. (Full precision values must be used.)

The line we have found is at the desired angle measured CCW from the point of intersection with the given line. If you allow the line to have that angle measured CW from the point of intersection, then the slope will be 7/9, and the equation will be ...

y = 7/9x -3

Sagot :

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