What is the general solution for 170=(90^2)/(16)sin(x)cos(x) ?

The general solution for 170=(90^2)/(16)sin(x)cos(x) is x=(0.73637…)/2+pin,x= pi/2-(0.73637…)/2+pin

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170=(90^2)/(16)sin(x)cos(x)

170 = \frac{9 0 ^{2}}{16} sin (x) cos (x)

x = \frac{0.73637 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.73637 \dots}{2} + πn

Solution steps

170 = \frac{9 0 ^{2}}{16} sin (x) cos (x)

Switch sides

\frac{9 0 ^{2}}{16} sin (x) cos (x) = 170

Rewrite using trig identities

\frac{sin ( 2 x )}{2} \cdot \frac{9 0 ^{2}}{16} = 170

Simplify

\frac{sin ( 2 x )}{2} \cdot \frac{9 0 ^{2}}{16} : \frac{2025 sin ( 2 x )}{8}

\frac{2025 sin ( 2 x )}{8} = 170

Multiply both sides by

8

2025 sin (2 x) = 1360

Divide both sides by

2025

sin (2 x) = \frac{272}{405}

Apply trig inverse properties

2 x = arcsin (\frac{272}{405}) + 2 πn, 2 x = π - arcsin (\frac{272}{405}) + 2 πn

Solve

2 x = arcsin (\frac{272}{405}) + 2 πn : x = \frac{arcsin ( \frac{272}{405} )}{2} + πn

Solve

2 x = π - arcsin (\frac{272}{405}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{272}{405} )}{2} + πn

x = \frac{arcsin ( \frac{272}{405} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{272}{405} )}{2} + πn

Show solutions in decimal form

x = \frac{0.73637 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.73637 \dots}{2} + πn

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

sin (x - \frac{π}{3}) = 0

\frac{- 2 + 3}{2} = - 1 + cos (4 θ + 135)

sin (2 x) = \frac{( 3 m - 2 )}{8}

sin (θ) = \frac{3}{7}

What is the general solution for 170=(90^2)/(16)sin(x)cos(x) ?
The general solution for 170=(90^2)/(16)sin(x)cos(x) is x=(0.73637…)/2+pin,x= pi/2-(0.73637…)/2+pin