What is the general solution for 4sin^2(r)-sin(r)=0 ?

The general solution for 4sin^2(r)-sin(r)=0 is r=0.25268…+2pin,r=pi-0.25268…+2pin,r=2pin,r=pi+2pin

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4sin^2(r)-sin(r)=0

4 sin^{2} (r) - sin (r) = 0

r = 0.25268 \dots + 2 πn, r = π - 0.25268 \dots + 2 πn, r = 2 πn, r = π + 2 πn

Solution steps

4 sin^{2} (r) - sin (r) = 0

Solve by substitution

sin (r) = \frac{1}{4}, sin (r) = 0

sin (r) = \frac{1}{4} : r = arcsin (\frac{1}{4}) + 2 πn, r = π - arcsin (\frac{1}{4}) + 2 πn

sin (r) = 0 : r = 2 πn, r = π + 2 πn

Combine all the solutions

r = arcsin (\frac{1}{4}) + 2 πn, r = π - arcsin (\frac{1}{4}) + 2 πn, r = 2 πn, r = π + 2 πn

Show solutions in decimal form

r = 0.25268 \dots + 2 πn, r = π - 0.25268 \dots + 2 πn, r = 2 πn, r = π + 2 πn

tan (θ) = \frac{3}{- 3}

cos (a) = 0.24

sin (x) = 1 5^{\circ}

cos (a) = 0.42

\frac{6}{sin ( 6 0 ^{\circ} )} = \frac{4}{sin ( x )}

What is the general solution for 4sin^2(r)-sin(r)=0 ?
The general solution for 4sin^2(r)-sin(r)=0 is r=0.25268…+2pin,r=pi-0.25268…+2pin,r=2pin,r=pi+2pin