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

The general solution for 4sin(2x)=3sin(x) is x=2pin,x=pi+2pin,x=1.18639…+2pin,x=2pi-1.18639…+2pin

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4sin(2x)=3sin(x)

4 sin (2 x) = 3 sin (x)

x = 2 πn, x = π + 2 πn, x = 1.18639 \dots + 2 πn, x = 2 π - 1.18639 \dots + 2 πn

Solution steps

4 sin (2 x) = 3 sin (x)

Subtract

3 sin (x)

from both sides

4 sin (2 x) - 3 sin (x) = 0

Rewrite using trig identities

- 3 sin (x) + 8 cos (x) sin (x) = 0

Factor

- 3 sin (x) + 8 cos (x) sin (x) : sin (x) (8 cos (x) - 3)

sin (x) (8 cos (x) - 3) = 0

Solving each part separately

sin (x) = 0 or 8 cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

8 cos (x) - 3 = 0 : x = arccos (\frac{3}{8}) + 2 πn, x = 2 π - arccos (\frac{3}{8}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arccos (\frac{3}{8}) + 2 πn, x = 2 π - arccos (\frac{3}{8}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.18639 \dots + 2 πn, x = 2 π - 1.18639 \dots + 2 πn

sin (a) = 0.1245

x, sin (x + z) = cos (y + z)

y, tan (y) = \frac{94}{152} c m

(sin (x) - 1) (sin (x) - 4) = 0

cos^{2} (a) = \frac{1}{5}

What is the general solution for 4sin(2x)=3sin(x) ?
The general solution for 4sin(2x)=3sin(x) is x=2pin,x=pi+2pin,x=1.18639…+2pin,x=2pi-1.18639…+2pin