Question 5:

Convert the following in the polar form :

Answer

Let r cos θ = −1 and r sin θ = 1

On squaring and adding, we obtain

r²(cos² θ + sin² θ) = 1 + 1

⇒ r²(cos² θ + sin² θ) = 1 + 1

⇒ r²(cos² θ + sin² θ) = 2

⇒ r² = 2                      [cos² θ + sin² θ = 1]

⇒ r = √2                  [Conventionally, r > 0]

∴ √2 cos θ = −1 and √2 sin θ = 1

Let r cos θ = −1 and r sin θ = 1

On squaring and adding, we obtain

r²(cos² θ + sin² θ)=1 + 1

⇒ r²(cos² θ + sin² θ) = 2

⇒ r² = 2                     [cos² θ + sin² θ = 1]

⇒ r = √2                  [Conventionally, r > 0]

∴ √2 cos θ =−1 and √2 sin θ = 1

This is the required polar form.

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