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Convert (7, 45°) to rectangular coordinates. Use exact values.

A) (7, 0)
B) (7, 7)
C) (7√2/2, 7√2/2)
D) (7√3/2, 7/2)

User Dgorti
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1 Answer

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Final answer:

The polar coordinates (7, 45°) can be converted to rectangular coordinates by using the formulas x = r * cos(θ) and y = r * sin(θ). The correct rectangular coordinates are (7√2/2, 7√2/2).

Step-by-step explanation:

To convert the polar coordinates (7, 45°) to rectangular coordinates, you can use the sine and cosine trigonometric functions, as the rectangular coordinates (x, y) can be found using the formulas x = r * cos(θ) and y = r * sin(θ) where r is the radius and θ is the angle in degrees.

To convert (7, 45°) to rectangular coordinates, we can use the formulas x = r * cos(θ) and y = r * sin(θ), where r is the magnitude (7) and θ is the angle (45°).

Plugging in the values, we get x = 7 * cos(45°) = 7 * (√2/2) = 7√2/2, and y = 7 * sin(45°) = 7 * (√2/2) = 7√2/2.

Therefore, the rectangular coordinates are (7√2/2, 7√2/2). So, the correct answer is C) (7√2/2, 7√2/2).

In this case, for r = 7 and θ = 45°:

  • x = 7 * cos(45°) = 7 * √2/2
  • y = 7 * sin(45°) = 7 * √2/2

Therefore, the rectangular coordinates are (7√2/2, 7√2/2), which corresponds to choice C.

User Earachefl
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