What is the general solution for (sin(x)+sin^2(x))/2 =0.5 ?

The general solution for (sin(x)+sin^2(x))/2 =0.5 is x=0.66623…+2pin,x=pi-0.66623…+2pin

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(sin(x)+sin^2(x))/2 =0.5

\frac{sin ( x ) + sin ^{2} ( x )}{2} = 0.5

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Solution steps

\frac{sin ( x ) + sin ^{2} ( x )}{2} = 0.5

Solve by substitution

sin (x) = \frac{- 1 + 5}{2}, sin (x) = - \frac{1 + 5}{2}

sin (x) = \frac{- 1 + 5}{2} : x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = - \frac{1 + 5}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

cos (b) = \frac{3}{5}

arctan (1 - x) + arctan (1 + x) = arctan (\frac{1}{8})

5 sin (4 x) = 2

2 cos^{2} (x) - 3 \cdot sin^{2} (x) - 2 = 0

x, lo g_{10} (y) = arctan (x) + c

What is the general solution for (sin(x)+sin^2(x))/2 =0.5 ?
The general solution for (sin(x)+sin^2(x))/2 =0.5 is x=0.66623…+2pin,x=pi-0.66623…+2pin