It is false that the value 5pi/4 is a solution for the given equation.
How to solve equation with trigonometry ratio ?
1. Collect the like terms
2. make the trigonometry ratio the subject of formula
3. Find the inverse of the trigonometry.
Given that a solution for the equation 3[tex]\sqrt{2}[/tex] sinФ + 2 = -1.
Collect the like terms
3[tex]\sqrt{2}[/tex] Sin Ф = -1 - 2
3[tex]\sqrt{2}[/tex] SinФ = -3
Sin Ф = -3 / 3[tex]\sqrt{2}[/tex]
SinФ = -1/[tex]\sqrt{2}[/tex]
Rationalize the RHS
SinФ = -1/[tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex] /[tex]\sqrt{2}[/tex]
Sin Ф = -[tex]\sqrt{2}[/tex] /2
Sin Ф = - 0.707
Ф = [tex]Sin^{-1}[/tex](-0.707)
Ф = 45°
Change the degree to radian
45 x [tex]\pi[/tex]/180
[tex]\pi[/tex]/4
Therefore, it is false that the value 5pi/4 is a solution for the given equation.
Learn more about trigonometry here: https://brainly.com/question/24349828
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