# Convert Φ = π/4 to rectangular form?

rectangular form:

Note that:

rectangular form:

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To convert the polar coordinate ( \Phi = \frac{\pi}{4} ) to rectangular form, we use the following conversion formulas:

[ x = r \cdot \cos(\Phi) ] [ y = r \cdot \sin(\Phi) ]

Given that ( \Phi = \frac{\pi}{4} ), we substitute this value into the formulas.

[ x = r \cdot \cos\left(\frac{\pi}{4}\right) ] [ y = r \cdot \sin\left(\frac{\pi}{4}\right) ]

Since ( \frac{\pi}{4} ) corresponds to a 45-degree angle, we know that ( \cos\left(\frac{\pi}{4}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} ).

Therefore, substituting these values into the formulas:

[ x = r \cdot \frac{\sqrt{2}}{2} ] [ y = r \cdot \frac{\sqrt{2}}{2} ]

This implies that for ( r = 1 ) (which is often assumed if the magnitude ( r ) is not provided):

[ x = \frac{\sqrt{2}}{2} ] [ y = \frac{\sqrt{2}}{2} ]

Thus, the rectangular form of the polar coordinate ( \Phi = \frac{\pi}{4} ) is ( \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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