the following formula can be found in the literature: <mo fence="false" stretchy="false">| si

Ashly Harrell

Ashly Harrell

Answered question

2022-05-20

the following formula can be found in the literature: | sin ( z ) | 2 = sin ( x ) 2 + sinh ( y ) 2 , z=x+iy; x , y R .
I am wondering if there is a similar formular in polar coordinates, i.e. | sin ( r e i θ ) | = . . . ?

Answer & Explanation

Madisyn Avery

Madisyn Avery

Beginner2022-05-21Added 12 answers

r e i θ = r cos ( θ ) + i r sin ( θ ) , so
| sin ( r e i θ ) | 2 = sin ( r cos ( θ ) ) 2 + sinh ( r sin ( θ ) ) 2

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