The first thing to do is remove the coefficients of the side with the variable. This is done here by dividing by two, to give sin(2x) = 0.5. The next step is to remove the sine function; take the inverse sine of each side to give 2x = 30o (for degrees) or 2x = 0.5236 (for radians; equal to pi/6). Finally, remove the coefficient of x by dividing by 2 again. This gives 15o or 0.2618 (equal to pi/12). These are only the trivial solutions; all others can be found using predetermined formula.
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cos2x + 2sinx - 2 = 0 (1-2sin2x)+2sinx-2=0 -(2sin2x-2sinx+1)=0 -2sinx(sinx+1)=0 -2sinx=0 , sinx+1=0 sinx=0 , sinx=1 x= 0(pi) , pi/2 , pi
2sinx+1 equals 0
1
y = -6
Solve, using the Rule of 72 rate = 4%, years = 18, fv=$8,000. Solve for PV. Formula: PV = $1/(1+r) t PV = $8000/(1+.04) 18 PV = $8000/2.0258 3949.03 = $8000/2.20258