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Which is the standard form of the equation with ( p = 6, ϕ = π/3 )?

a. ( 6cos(π/3) + 6sin(π/3) = 0 )
b. ( 6cos(π/3) - 6sin(π/3) = 0 )
c. ( 6cos(π/3) + 6sin(π/3) = 1 )
d. ( 6cos(π/3) - 6sin(π/3) = 1 )

User Krankuba
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1 Answer

5 votes

Final answer:

The standard form of the equation with ( p = 6, φ = π/3 ) is not listed among the provided options. The proper form translates to r = 3 + 3*√3 or approximately r = 8.196 after converting to Cartesian coordinates.

Step-by-step explanation:

The question asks us to determine the standard form of the equation with parameters p = 6 and φ = π/3. When these parameters are applied to a polar equation of the form r = p, where r is the radius and φ is the angle in radians, we get the equation r(6) = 6. This equation equates to x = r*cos(φ) and y = r*sin(φ) in Cartesian coordinates, where x and y represent the horizontal and vertical axes, respectively. In this case, for φ = π/3, cos(π/3) is 1/2 and sin(π/3) is √3/2. Thus, our Cartesian coordinates become x = 6*(1/2) and y = 6*(√3/2), and plugging these values into the equation we obtain, 3 + 6*(√3/2) = r. The standard form of the equation is r = 3 + 6*(√3/2) which simplifies to r = 3 + 3√3 or approximately r = 8.196. None of the answer choices provided are correct since they do not represent this standard form.

User Jay Dansand
by
8.3k points

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