Solve the Equation (X in Radians and θ in Degrees) $4 \csc ^ { 2 } \theta = 5 \csc \theta$

question 351

Multiple Choice

Solve the equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth.
- $4 \csc ^ { 2 } \theta = 5 \csc \theta$

• A) \(\left\{ 0 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 53.1 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 126.9 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 180 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• B) \(\left\{ 0 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 53.1 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 126.9 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 233.1 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• C)
• \(\left\{ 53.1 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 126.9 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• D)
• \(\left\{ 0 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 53.1 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 126.9 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)

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Definitions:

Hypothalamus

A region of the brain below the thalamus that coordinates both the autonomic nervous system and the activity of the pituitary, controlling body temperature, thirst, hunger, and other homeostatic systems.

Amygdala

A region of the brain within the temporal lobe, crucial for the processing of emotions, especially fear and pleasure.

Temporal Lobes

Regions of the cerebral cortex below the parietal lobes and in front of the occipital lobes; these regions are important for hearing and for recognizing objects, such as faces.

Cerebral Cortex

The outer layer of the brain, responsible for complex behaviors, thought, memory, and consciousness.