Solve the Equation (X in Radians and in Degrees) for All

question 43

Multiple Choice

Solve the equation (x in radians and 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.
- $3 \csc ^ { 2 } \theta = 4 \csc \theta$

• A) \(\left\{ 0 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 48.6 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 131.4 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 228.6 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• B) \(\left\{ 0 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 48.6 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 131.4 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 180 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• C) \(\left\{ 0 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 48.6 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 131.4 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• D) \(\left\{ 48.6 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 131.4 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)

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Definitions:

Nash Equilibrium

A state in strategic interactions where each participant's chosen strategy leaves them with no incentive to deviate, given the choices of others.

Cournot Model

A economic model describing an industry structure in which companies compete on the quantity of output they decide to produce, assuming their rivals' decisions are fixed.

Bertrand Model

An economic model of competition among firms, where firms choose prices rather than quantities to compete.

Collude

The act of cooperating or conspiring, especially between competitors, to achieve a mutual benefit such as setting prices.