Solve the Equation (X in Radians and θ in Degrees) $\tan x ( \tan x - 2 ) = 7$

question 404

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.
- $\tan x ( \tan x - 2 ) = 7$

• A) \(\{ 1.3153 + \mathrm { n } \pi , 5.2129 + \mathrm { n } \pi \}\)
• B) \(\{ 1.2608 + \mathrm { n } \pi , 2.2991 + \mathrm { n } \pi \}\)
• C) \(\{ 1.3153 + \mathrm { n } \pi , 2.0713 + \mathrm { n } \pi \}\)
• D) \(\{ 1.2608 + \mathrm { n } \pi , 5 + \mathrm { n } \pi \}\)

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Definitions:

Stackelberg

A model of a market in which one leader firm sets its output first, and then other firms follow, adjusting their outputs accordingly, in strategic game theory.

Cournot Model

A model in oligopoly theory where firms compete on the quantity of output they decide independently and simultaneously.

Monopolistic Competition

A market structure characterized by many firms selling products that are similar but not identical, allowing for competition on factors other than just price, such as quality and marketing.

Bertrand Model

Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge.