please i need help please help me

Question

why there are exactly two angles between 0 and 360 that have the same tangent ratio. 

Answer 1

The period of the tangent is π^r. Therefore for every angle in QI there is an angle in QIII with the same tangent value. Likewise for angles in QII ad QIV.

Answer 2

tangent of an angle = ratio of opposite side divided by adjacent side of a right triangle angle formed in a unit circle where radius = the hypotenuse of the right angle = 1

For a specific example, if the tangent of an angle = tanA = sqr3 = sqr3/2 divided by 1/2, there are two angles A that satsify that equation, where 0<A<360. A = 60 degrees and A = 180+60= 240 degrees.

tangents >0 in quadrants I & III

tangents <0 in quadrants II & IV

more generally, if A = tan^-1(sqr3) then A=60+180n where n= any integer

so A = 60, 240, 420, 600, ... 60n where n = any integer

and A = -120, - 300, -480, -660, .... 60n where n = any integer

There's an infinite number of angles that satsify the equation A=tan^-1(sqr3), but if you limit A to 0<A<360 there are two and only two angles that satisfy the equation.

whatever number you pick for y, with tanA = y, there are exactly two values of A between 0 and 360, that satisfy the equation tanA = y. And one value of A will be in quadrant I and the other in quadrant III, if tanA>0, or one value of A will be in quadrant II and the other in quadrant IV, if tanA<0