Solve the Equation in the Interval [0°, 360°) $\sin 2 \theta = - \sin \theta$

question 113

Multiple Choice

Solve the equation in the interval [0°, 360°) . Give solutions to the nearest tenth, if necessary.
- $\sin 2 \theta = - \sin \theta$

• A) \(\left\{ 0 ^ { \circ } , 60 ^ { \circ } , 120 ^ { \circ } , 180 ^ { \circ } , 240 ^ { \circ } , 300 ^ { \circ } \right\}\)
• B) \(\left\{ 60 ^ { \circ } , 120 ^ { \circ } , 240 ^ { \circ } , 300 ^ { \circ } \right\}\)
• C) \(\left\{ 0 ^ { \circ } , 180 ^ { \circ } \right\}\)
• D) \(\left\{ 0 ^ { \circ } , 120 ^ { \circ } , 180 ^ { \circ } , 240 ^ { \circ } \right\}\)

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Definitions:

Doublet

A pattern observed in NMR spectroscopy, indicating two adjacent hydrogen atoms influencing the resonance of another hydrogen or group.

Off-Resonance Decoupled

A technique in NMR spectroscopy where decoupling is applied at a frequency offset from the resonance frequency of the nucleus of interest to simplify spectra.

Multiplicities

In nuclear magnetic resonance (NMR) spectroscopy, multiplicities refer to the splitting pattern of a signal, indicating the number of nearby hydrogens (or other nuclei) interacting with the observed nucleus.

Molecular Formula

A representation of the actual number and type of atoms in a molecule, without indicating the structure or arrangement.