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Convert the polar coordinates to its equ...

Convert the polar coordinates to its equivalent Cartesian coordinates`(2,pi)`.

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To convert the polar coordinates (2, π) to Cartesian coordinates, we will follow these steps: ### Step 1: Identify the polar coordinates The polar coordinates are given as (r, θ) where: - r = 2 - θ = π ### Step 2: Use the conversion formulas The conversion from polar coordinates to Cartesian coordinates (x, y) is done using the following formulas: - \( x = r \cdot \cos(\theta) \) - \( y = r \cdot \sin(\theta) \) ### Step 3: Substitute the values of r and θ Now, we will substitute the values of r and θ into the formulas: - \( x = 2 \cdot \cos(\pi) \) - \( y = 2 \cdot \sin(\pi) \) ### Step 4: Calculate the cosine and sine values We know the following trigonometric values: - \( \cos(\pi) = -1 \) - \( \sin(\pi) = 0 \) ### Step 5: Calculate x and y Now, we can calculate the values of x and y: - \( x = 2 \cdot (-1) = -2 \) - \( y = 2 \cdot 0 = 0 \) ### Step 6: Write the Cartesian coordinates Thus, the Cartesian coordinates corresponding to the polar coordinates (2, π) are: - \( (x, y) = (-2, 0) \) ### Final Answer The equivalent Cartesian coordinates are \( (-2, 0) \). ---

To convert the polar coordinates (2, π) to Cartesian coordinates, we will follow these steps: ### Step 1: Identify the polar coordinates The polar coordinates are given as (r, θ) where: - r = 2 - θ = π ### Step 2: Use the conversion formulas ...
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