What is the general solution for sin^2(3a)=0.56 ?

The general solution for sin^2(3a)=0.56 is

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sin^2(3a)=0.56

sin^{2} (3 a) = 0.56

a = \frac{0.84554 \dots}{3} + \frac{2 πn}{3}, a = \frac{π}{3} - \frac{0.84554 \dots}{3} + \frac{2 πn}{3}, a = - \frac{0.84554 \dots}{3} + \frac{2 πn}{3}, a = \frac{π}{3} + \frac{0.84554 \dots}{3} + \frac{2 πn}{3}

Solution steps

sin^{2} (3 a) = 0.56

Solve by substitution

sin (3 a) = 0.56, sin (3 a) = - 0.56

sin (3 a) = 0.56 : a = \frac{arcsin ( 0.56 )}{3} + \frac{2 πn}{3}, a = \frac{π}{3} - \frac{arcsin ( 0.56 )}{3} + \frac{2 πn}{3}

sin (3 a) = - 0.56 : a = - \frac{arcsin ( \frac{14}{5} )}{3} + \frac{2 πn}{3}, a = \frac{π}{3} + \frac{arcsin ( 0.56 )}{3} + \frac{2 πn}{3}

Combine all the solutions

a = \frac{arcsin ( 0.56 )}{3} + \frac{2 πn}{3}, a = \frac{π}{3} - \frac{arcsin ( 0.56 )}{3} + \frac{2 πn}{3}, a = - \frac{arcsin ( \frac{14}{5} )}{3} + \frac{2 πn}{3}, a = \frac{π}{3} + \frac{arcsin ( 0.56 )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

a = \frac{0.84554 \dots}{3} + \frac{2 πn}{3}, a = \frac{π}{3} - \frac{0.84554 \dots}{3} + \frac{2 πn}{3}, a = - \frac{0.84554 \dots}{3} + \frac{2 πn}{3}, a = \frac{π}{3} + \frac{0.84554 \dots}{3} + \frac{2 πn}{3}

cos (x) = 0.22

3 cos (b) - 1 = 5 cos (b) + 1

sin (- x) = cos (x)

tan (a) = \frac{- 4}{3}

cot (x) - 2 tan (x) = - 0.25

What is the general solution for sin^2(3a)=0.56 ?
The general solution for sin^2(3a)=0.56 is