What is the general solution for 1/32*1200^2*sin(2θ)=3000 ?

The general solution for 1/32*1200^2*sin(2θ)=3000 is θ=(0.06671…)/2+pin,θ= pi/2-(0.06671…)/2+pin

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1/321200^2sin(2θ)=3000

\frac{1}{32} \cdot 120 0^{2} \cdot sin (2 θ) = 3000

θ = \frac{0.06671 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.06671 \dots}{2} + πn

Solution steps

\frac{1}{32} \cdot 120 0^{2} sin (2 θ) = 3000

Simplify

\frac{1}{32} \cdot 120 0^{2} : 45000

45000 sin (2 θ) = 3000

Divide both sides by

45000

sin (2 θ) = \frac{1}{15}

Apply trig inverse properties

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

Solve

2 θ = arcsin (\frac{1}{15}) + 2 πn : θ = \frac{arcsin ( \frac{1}{15} )}{2} + πn

Solve

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

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

Show solutions in decimal form

θ = \frac{0.06671 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.06671 \dots}{2} + πn

1 - cos^{2} (a) = sin^{2} (2 a)

4 cos (2 x) = - 2 sin (x)

tan^{2} (θ) + 2 tan (θ) = 0, tan (2 θ) + 2 tan (θ) = 0

2 cot (x) csc (x) - csc^{2} (x) = 0

8 tan (a) + 3 = 2 tan (a) + 3

What is the general solution for 1/32*1200^2*sin(2θ)=3000 ?
The general solution for 1/32*1200^2*sin(2θ)=3000 is θ=(0.06671…)/2+pin,θ= pi/2-(0.06671…)/2+pin