Ask Question
12 July, 05:43

2 sin^2 + sin x - 3 = 0

+2
Answers (1)
  1. 12 July, 05:53
    0
    x = 2 π n_1 + π/2 for n_1 element Z

    or x = π + sin^ (-1) (3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^ (-1) (3/2) for n_3 element Z

    Step-by-step explanation:

    Solve for x:

    -3 + sin (x) + 2 sin^2 (x) = 0

    The left hand side factors into a product with two terms:

    (sin (x) - 1) (2 sin (x) + 3) = 0

    Split into two equations:

    sin (x) - 1 = 0 or 2 sin (x) + 3 = 0

    Add 1 to both sides:

    sin (x) = 1 or 2 sin (x) + 3 = 0

    Take the inverse sine of both sides:

    x = 2 π n_1 + π/2 for n_1 element Z

    or 2 sin (x) + 3 = 0

    Subtract 3 from both sides:

    x = 2 π n_1 + π/2 for n_1 element Z

    or 2 sin (x) = - 3

    Divide both sides by 2:

    x = 2 π n_1 + π/2 for n_1 element Z

    or sin (x) = - 3/2

    Take the inverse sine of both sides:

    Answer: x = 2 π n_1 + π/2 for n_1 element Z

    or x = π + sin^ (-1) (3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^ (-1) (3/2) for n_3 element Z
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “2 sin^2 + sin x - 3 = 0 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers