For what values of θ, −π ≤ θ ≤ π, is y = tan θ undefined?

Answer:The answer is II and IV ⇒ the 3rd answerStep-by-step explanation:* lets check the domain of angle Ф∵ -π ≤ Ф ≤ π∵ y = tanФ ∵ tanФ = sinФ/cosФ* The effective term which makes tanФ undefined is cosФ- If cosФ = 0, than tanФ will be undefined* Lets check the angles that have cosФ = 0∵ The unit circle intersect x-axis at point (1 , 0) and (-1 , 0)∵ The unit circle intersect y-axis at point (0 , 1) and (0 , -1)∵ cosФ = x-coordinates of the points∵ The points of intersection with the y-axis have x- coordinates = 0∴ The angles on the y-axis have cosФ = 0* The angles on the +ve part of y-axis are π/2 and -3π/2  The angles on the -ve part of y-axis are -π/2 and 3π/2 ∴ The tan of π/2 , 3π/2 , -π/2 , -3π/2 undefined* In the problemI. -π ⇒ defined ⇒ on the -ve part of x-axisII. -π/2 ⇒undefinedIII. 0 ⇒ defined ⇒ on the +ve part of the x-axisIV. π/2 ⇒ undefinedV. π ⇒ defined ⇒ on the -ve part of x-axis∴ The answer is II and IV ⇒ the 3rd answer