Question

Find all polar coordinates of point P = (6, 31°).

Answer 1

Answer:

P = 5.143 + i 3.090

Step-by-step explanation:

∵ Z = a + i b = (r , Ф)

∵ a = r cosФ and b = r sinФ

∵ r = $\sqrt{a^{2}+b^{2}}$

∵ P = (6 , 31°)

∴ P = 6(cos31 + i sin31)

      = 6cos31 + i (6sin31) = 5.143 + i 3.090

OR

∵ a² + b² = (6)² ⇒ a² + b² = 36 ⇒ (1)

∵ b/a = tanФ ⇒ b/a = tan31

∴ b = a tan31 ⇒ (2)

Substitute (2) in (1)

∴ a² + a² tan²31 = 36 ⇒ a²(1 + tan²31) = 36

∴ a² = 36/(1 + tan²31) = 26.45

∴ a = 5.143

∴ b = 5.143 × tan31 = 3.090

∴ P = 5.14 + i 3.090