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

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

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step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.