Trigonometry help

Question

If tan(θ)=85 , where 0≤θ≤2π. Largest positive value of θ

Answer 1

Tangent is positive in quadrants 1 and 3 and since we are looking for the largest possible angle, we would want to look in Q3.

tan(θ) = 85 so, taking the tangent inverse of both sides yields:

tan^-1[tan(θ)] = tan^-1[85]

θ = tan^-1(85)

Using your calculator (in radian mode) and plugging in tan^-1(85) you get θ = 1.55 radians however this is the angle that is in Q1. To find the angle that is in Q3, add π radians. 1.55 + π = 4.70 radians