What is the general solution for 5sin(2x-pi/2)=0.5 ?

The general solution for 5sin(2x-pi/2)=0.5 is x=pin+pi/4+(0.10016…)/2 ,x=pin+pi/2+pi/4-(0.10016…)/2

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5sin(2x-pi/2)=0.5

5 sin (2 x - \frac{π}{2}) = 0.5

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

Solution steps

5 sin (2 x - \frac{π}{2}) = 0.5

Divide both sides by

5

sin (2 x - \frac{π}{2}) = 0.1

Apply trig inverse properties

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn, 2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

Solve

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn : x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

Solve

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn : x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

Show solutions in decimal form

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

5 sin (x) = 3 sin (x) + cos (x)

3 - 3 cos (5 x) = 3 cos (5 x)

6 tan^{2} (θ) + 11 tan (θ) = 4 tan (θ) - 2

\frac{1}{1 - cos ( x )} + \frac{1}{1 + cos ( x )} = 2 sec^{2} (x)

2 cos^{2} (θ) - sin (θ) = 2

What is the general solution for 5sin(2x-pi/2)=0.5 ?
The general solution for 5sin(2x-pi/2)=0.5 is x=pin+pi/4+(0.10016…)/2 ,x=pin+pi/2+pi/4-(0.10016…)/2