SOLUTION: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 5 − 12i So far I have gotten 13(cos(22.03)+isin(22.03), and 13(cos(21.83

Algebra ->  Trigonometry-basics -> SOLUTION: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 5 − 12i So far I have gotten 13(cos(22.03)+isin(22.03), and 13(cos(21.83      Log On


   

Question 1170517: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
5 − 12i
So far I have gotten 13(cos(22.03)+isin(22.03), and 13(cos(21.83)+isin(21.83).
All incorrect.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw it out on a coordinate grid, using the x-axis for reals and the y-axis for imaginary parts you will put a point at (5,-12).


Now:
+theta+=+tan%5E-1%28-12%2F5%29+=+-67.38%5Eo+
And the modulus (magnitude or radius for polar form) is equal to the hypotenuse of the drawn triangle:
+sqrt%285%5E2+%2B+%28-12%29%5E2%29+=+13+
Putting these together:
+highlight%28+z+=+13+%28cos%28-67.38%5Eo%29+%2B+i+%2A+sin%28-67.38%5Eo%29%29+%29+

Noting that -67.38 degrees (CW rotation of 67.38 degrees) is the same as a CCW rotation of 292.62 degrees, you can write:
+highlight%28+z+=+13+%28cos%28292.62%5Eo%29+%2B+i+%2A+sin%28292.62%5Eo%29%29+%29+
While the negative angle might be a little more common, both answers should be acceptable.