Fifth 3871

What is the sum of the fifth root of 243?

Correct answer:

s = 0

Step-by-step explanation:

a = 5243 = 3 α = \frac{2 π}{5} = \frac{2 \cdot 3 . 1 4 1 6}{5} ≐ 1.2566 rad x_{1} = a \cdot cos (0 \cdot α) = 3 \cdot cos (0 \cdot 1.2566) = 3 x_{2} = a \cdot cos (1 \cdot α) = 3 \cdot cos (1 \cdot 1.2566) ≐ 0.9271 x_{3} = a \cdot cos (2 \cdot α) = 3 \cdot cos (2 \cdot 1.2566) ≐ - 2.4271 x_{4} = a \cdot cos (3 \cdot α) = 3 \cdot cos (3 \cdot 1.2566) ≐ - 2.4271 x_{5} = a \cdot cos (4 \cdot α) = 3 \cdot cos (4 \cdot 1.2566) ≐ 0.9271 x = x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 3 + 0.9271 + (- 2.4271) + (- 2.4271) + 0.9271 = 0 y_{1} = a \cdot sin (0 \cdot α) = 3 \cdot sin (0 \cdot 1.2566) = 0 y_{2} = a \cdot sin (1 \cdot α) = 3 \cdot sin (1 \cdot 1.2566) ≐ 2.8532 y_{3} = a \cdot sin (2 \cdot α) = 3 \cdot sin (2 \cdot 1.2566) ≐ 1.7634 y_{4} = a \cdot sin (3 \cdot α) = 3 \cdot sin (3 \cdot 1.2566) ≐ - 1.7634 y_{5} = a \cdot sin (4 \cdot α) = 3 \cdot sin (4 \cdot 1.2566) ≐ - 2.8532 y = y_{1} + y_{2} + y_{3} + y_{4} + y_{5} = 0 + 2.8532 + 1.7634 + (- 1.7634) + (- 2.8532) = 1.0036 \cdot 1 0^{- 13} s = x + i \cdot y s = 0

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Try our complex numbers calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

angle

Grade of the word problem:

high school

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: