What is the general solution for 4sin(pi/2 x)=3 ?

The general solution for 4sin(pi/2 x)=3 is x=(2*0.84806…)/pi+4n,x=2-(2*0.84806…)/pi+4n

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4sin(pi/2 x)=3

4 sin (\frac{π}{2} x) = 3

x = \frac{2 \cdot 0.84806 \dots}{π} + 4 n, x = 2 - \frac{2 \cdot 0.84806 \dots}{π} + 4 n

Solution steps

4 sin (\frac{π}{2} x) = 3

Divide both sides by

4

sin (\frac{π}{2} x) = \frac{3}{4}

Apply trig inverse properties

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn, \frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn

Solve

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn : x = \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

Solve

\frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn : x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

x = \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n, x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

Show solutions in decimal form

x = \frac{2 \cdot 0.84806 \dots}{π} + 4 n, x = 2 - \frac{2 \cdot 0.84806 \dots}{π} + 4 n

1 + cos (θ) = 2 cos (θ)

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

tan (2 t) = 0

3 cos (4 x - 26) + 5 = 7

cos (θ) = 9

What is the general solution for 4sin(pi/2 x)=3 ?
The general solution for 4sin(pi/2 x)=3 is x=(2*0.84806…)/pi+4n,x=2-(2*0.84806…)/pi+4n