Find All Solutions to the Equation $4 \sin ^ { 2 } x - 4 \sin x + 1 = 0$

question 34

Multiple Choice

Find all solutions to the equation.
- $4 \sin ^ { 2 } x - 4 \sin x + 1 = 0$

• A) \(\left\{ \frac { \pi } { 6 } + 2 \mathrm { n } \pi , \frac { 7 \pi } { 6 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}\)
• B) \(\left\{ \frac { \pi } { 6 } + 2 \mathrm { n } \pi , \frac { 5 \pi } { 6 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}\)
• C) \(\left\{ \frac { \pi } { 3 } + 2 \mathrm { n } \pi , \frac { 5 \pi } { 3 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \right\}\)
• D) \(\left\{ \frac { \pi } { 6 } + 2 \mathrm { n } \pi , \frac { 11 \pi } { 6 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \right\}\)

---

Definitions:

Compulsive Behavior Therapy

A type of therapy focusing on identifying and changing harmful compulsive behaviors through various techniques, including cognitive-behavioral therapy.

Counter-Blocking Therapy

A treatment approach intended to counteract or neutralize the effects of another therapy, often used in reference to managing side effects.

Dysthymia

A persistent, mild depression lasting for a long period, often years.

Mild Bipolar Disorder

A less severe form of bipolar disorder characterized by less extreme mood swings between depression and mania.