What is the general solution for (sin(pi/2))/5 =(sin(x))/4 ?

The general solution for (sin(pi/2))/5 =(sin(x))/4 is x=0.92729…+2pin,x=pi-0.92729…+2pin

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(sin(pi/2))/5 =(sin(x))/4

\frac{sin ( \frac{π}{2} )}{5} = \frac{sin ( x )}{4}

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

Solution steps

\frac{sin ( \frac{π}{2} )}{5} = \frac{sin ( x )}{4}

sin (\frac{π}{2}) = 1

\frac{1}{5} = \frac{sin ( x )}{4}

Switch sides

\frac{sin ( x )}{4} = \frac{1}{5}

Multiply both sides by

4

sin (x) = \frac{4}{5}

Apply trig inverse properties

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

cos (3 x - 1) = \frac{1}{2}

tan^{2} (x) = sec (x) + 1

cos (u) = \frac{2}{5}, cos (2 u)

sin (b) = \frac{2}{2}

h = 7 cos (\frac{π}{3} t), t

What is the general solution for (sin(pi/2))/5 =(sin(x))/4 ?
The general solution for (sin(pi/2))/5 =(sin(x))/4 is x=0.92729…+2pin,x=pi-0.92729…+2pin