Write the complex number 3(\cos 210+i \sin 210) in rectangular

Lizeth Jackson

Lizeth Jackson

Answered question

2022-01-30

Write the complex number 3(cos210+isin210) in rectangular form?

Answer & Explanation

trasahed

trasahed

Beginner2022-01-31Added 14 answers

cos210=cos(180+30)=cos30=32.
sin210=sin(180+30)=sin30=12.
3(cos210+isin210)=3(32)+3i(12)
(32)3(32)i
My favourite way of seeing that sin30=12and cos30=32 is to picture an equilateral triangle with sides of length 1. This will have internal angles all 60 degrees (so the three angles add up to 180 degrees. Then cut the triangle in two to make two right-angled triangles. These will have internal angles of 30, 60 and 90 degrees. The shortest side (opposite the 30 degree angle) will have length 12 and the other side at right angles, will have length
12(12)2=114=34=32.

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