Find the Exact Solutions of the Given Equation in the Interval

question 223

Multiple Choice

Find the exact solutions of the given equation in the interval $[ 0,2 \pi )$ . sin 4x= -2sin 2x

• A) \(x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }\)
• B) \(x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 }\)
• C) \(x = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }\)
• D) \(x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }\)
• E) \(x = \frac { 7 \pi } { 6 } , \frac { 3 \pi } { 2 } , \frac { 11 \pi } { 6 }\)

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Definitions:

RLC Parallel Circuit

An electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) all connected in parallel, affecting the overall impedance differently from a series circuit.

Applied Voltage

The voltage that is applied across a component or circuit from an external source, driving current through it.

Parallel Resonant Circuits

Circuits where components are connected in parallel, bringing the circuit to resonance at a specific frequency where the inductive and capacitive reactances are equal in magnitude but opposite in phase.

Q

In electrical and electronic engineering, Q or quality factor refers to the measure of the efficiency of a reactive component, such as an inductor or capacitor, representing the ratio of stored vs. dissipated energy per cycle.