Answer:
The answer is II and IV ⇒ the 3rd answer
Step-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 problem
I. -π ⇒ defined ⇒ on the -ve part of x-axis
II. -π/2 ⇒undefined
III. 0 ⇒ defined ⇒ on the +ve part of the x-axis
IV. π/2 ⇒ undefined
V. π ⇒ defined ⇒ on the -ve part of x-axis
∴ The answer is II and IV ⇒ the 3rd answer
