What is the general solution for 300= 1/32 100^2sin(2x) ?

The general solution for 300= 1/32 100^2sin(2x) is x=(1.28700…)/2+pin,x= pi/2-(1.28700…)/2+pin

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300= 1/32 100^2sin(2x)

300 = \frac{1}{32} 10 0^{2} sin (2 x)

x = \frac{1.28700 \dots}{2} + πn, x = \frac{π}{2} - \frac{1.28700 \dots}{2} + πn

Solution steps

300 = \frac{1}{32} \cdot 10 0^{2} sin (2 x)

Switch sides

\frac{1}{32} \cdot 10 0^{2} sin (2 x) = 300

Simplify

\frac{1}{32} \cdot 10 0^{2} : \frac{625}{2}

\frac{625}{2} sin (2 x) = 300

Multiply both sides by

2

625 sin (2 x) = 600

Divide both sides by

625

sin (2 x) = \frac{24}{25}

Apply trig inverse properties

2 x = arcsin (\frac{24}{25}) + 2 πn, 2 x = π - arcsin (\frac{24}{25}) + 2 πn

Solve

2 x = arcsin (\frac{24}{25}) + 2 πn : x = \frac{arcsin ( \frac{24}{25} )}{2} + πn

Solve

2 x = π - arcsin (\frac{24}{25}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{24}{25} )}{2} + πn

x = \frac{arcsin ( \frac{24}{25} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{24}{25} )}{2} + πn

Show solutions in decimal form

x = \frac{1.28700 \dots}{2} + πn, x = \frac{π}{2} - \frac{1.28700 \dots}{2} + πn

sin^{2} (x) = \frac{45}{52}

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

\frac{π ^{2}}{8} sec^{2} (\frac{π x}{4}) tan (\frac{π x}{4}) = 0

sec (x) = \frac{2}{3}

arccos (x) = \frac{π}{4}

What is the general solution for 300= 1/32 100^2sin(2x) ?
The general solution for 300= 1/32 100^2sin(2x) is x=(1.28700…)/2+pin,x= pi/2-(1.28700…)/2+pin