SOLUTION: Solve the following equations for all x, unless the domain is restricted. sin^2(x) + sin(x) = 2, where 0 < x <2𝛑 A. x = 1, -2 B. x = 2𝛑/3 C. x = 𝛑/4 D. no solutio

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Question 1205834: Solve the following equations for all x, unless the domain is restricted.
sin^2(x) + sin(x) = 2, where 0 < x <2𝛑
A. x = 1, -2
B. x = 2𝛑/3
C. x = 𝛑/4
D. no solution
E. x = 𝛑/2
F. x = 𝛑/2, 4𝛑

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

, where





=>=> => no real solution
=>=>
=>general solution:

solution in given interval :



answer:
E. x = 𝛑/2

Answer by ikleyn(52943)   (Show Source): You can put this solution on YOUR website!
.


This equation is good to solve it mentally in your head, by applying reasoning.


Indeed, sin(x) by modulus is never greater than 1.


Therefore, if sin^2(x) + sin(x) = 2, it may happen ONLY if sin(x) = 1.


But then x =  is the only solution in the given interval.

Solved.



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