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
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 :
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.