What is the general solution for 2sin(2x+15)= 1/2 ?

The general solution for 2sin(2x+15)= 1/2 is x=pin-15/2+(0.25268…)/2 ,x=pin+pi/2-15/2-(0.25268…)/2

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2sin(2x+15)= 1/2

2 sin (2 x + 15) = \frac{1}{2}

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

Solution steps

2 sin (2 x + 15) = \frac{1}{2}

Divide both sides by

2

sin (2 x + 15) = \frac{1}{4}

Apply trig inverse properties

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Solve

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn : x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

Solve

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn : x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

Show solutions in decimal form

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

sin^{2} (x) - 2 cos^{4} (x) = 0

2 cos^{2} (θ) - 1 = sec (θ)

\frac{1}{sin ( x )} - sin (x) = sin (x)

4 cos^{2} (x) = 0

sin (2 x) = \frac{2 \cdot 10 \cdot 1500000}{11000000}

What is the general solution for 2sin(2x+15)= 1/2 ?
The general solution for 2sin(2x+15)= 1/2 is x=pin-15/2+(0.25268…)/2 ,x=pin+pi/2-15/2-(0.25268…)/2