Rectangular Form

Question

Change 2cis30° to exact rectangular form.

Answer 1

2cis(30⁰) = 2(cos(30⁰)+isin(30⁰)

the cosine of 30 degrees will be equal to √3/2 and the sine will be 1/2. (how do we know this? Take an equilateral triangle, where all of the angles will be 60 degrees and bisect one of the angles; you'll essentially turn the equilateral triangle into two right triangles with angles of 30, 60 and of course 90 degrees. Use the definition of cosine and sine and you can confirm that).

2cis(30⁰) = 2(cos(30⁰)+isin(30⁰) = 2(√3/2 + i1/2) = √3+i