What is the general solution for 170=(160^2)/(32)sin(2θ) ?

The general solution for 170=(160^2)/(32)sin(2θ) is θ=(0.21413…)/2+pin,θ= pi/2-(0.21413…)/2+pin

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170=(160^2)/(32)sin(2θ)

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

θ = \frac{0.21413 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.21413 \dots}{2} + πn

Solution steps

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

Switch sides

\frac{16 0 ^{2}}{32} sin (2 θ) = 170

Simplify

\frac{16 0 ^{2}}{32} : 800

800 sin (2 θ) = 170

Divide both sides by

800

sin (2 θ) = \frac{17}{80}

Apply trig inverse properties

2 θ = arcsin (\frac{17}{80}) + 2 πn, 2 θ = π - arcsin (\frac{17}{80}) + 2 πn

Solve

2 θ = arcsin (\frac{17}{80}) + 2 πn : θ = \frac{arcsin ( \frac{17}{80} )}{2} + πn

Solve

2 θ = π - arcsin (\frac{17}{80}) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( \frac{17}{80} )}{2} + πn

θ = \frac{arcsin ( \frac{17}{80} )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( \frac{17}{80} )}{2} + πn

Show solutions in decimal form

θ = \frac{0.21413 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.21413 \dots}{2} + πn

sin (3 x) = 3 sin (x) cos (x)

sin (x) = \frac{2 π}{5}

sin (x) = \frac{2 π}{7}

cos (θ) sin (θ) = 0

6 cos (6 x - \frac{π}{6}) + 3 = 0

What is the general solution for 170=(160^2)/(32)sin(2θ) ?
The general solution for 170=(160^2)/(32)sin(2θ) is θ=(0.21413…)/2+pin,θ= pi/2-(0.21413…)/2+pin