Solve the Equation (X in Radians and θ in Degrees) $3 \cos ^ { 2 } \theta + 2 \cos \theta = 1$

question 159

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.
- $3 \cos ^ { 2 } \theta + 2 \cos \theta = 1$

• A) \(\left\{ 70.5 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 180 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 289.5 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• B) \(\left\{ 49.8 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 130.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 229.8 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 310.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• C) \(\left\{ 51.8 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 128.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)
• D) \(\left\{ 103.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 145.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 283.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } , 325.2 ^ { \circ } + 360 ^ { \circ } \mathrm { n } \right\}\)

---

Definitions:

Earthquake

Sudden movement of the earth caused by the abrupt release of energy.

Volcano

A vent in the surface of Earth through which magma and associated gases and ash erupt; also the form or structure, usually conical, that is produced by material erupted from the vent.

Landslide

A general term for the rapid downslope movement of soil, sediment, bedrock, or a mixture of these; also the material or landform formed by this process.

Global Climate

The average weather patterns that are observed over long periods, across the entire planet, encompassing a complex system influenced by solar radiation, the atmosphere, oceans, and landmasses.