6/pi-4sin^2(x)=0

Solution

\frac{6}{π} - 4 sin^{2} (x) = 0

x = 0.76285 \dots + 2 πn, x = π - 0.76285 \dots + 2 πn, x = - 0.76285 \dots + 2 πn, x = π + 0.76285 \dots + 2 πn

Solution steps

\frac{6}{π} - 4 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{3}{2 π}, sin (x) = - \frac{3}{2 π}

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

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.76285 \dots + 2 πn, x = π - 0.76285 \dots + 2 πn, x = - 0.76285 \dots + 2 πn, x = π + 0.76285 \dots + 2 πn

1 + 2 cos (x) + cos^{2} (x) = 3 sin^{2} (x)

L, sin (k L) = 0

cos (- x) = 2, sec (x) + cos (x)

2 \cdot sin (3 θ) = 2

cos (x) = \frac{9.8}{( 0.1 ) ( 6.28 ) ^{2}}