SOLUTION: Consider the graph of y = tan x (a)How does it show that the tangent of 90 degrees is undefined? (b)What are other undefined x values? (c)What is the value of the tangent of ang

Algebra ->  Trigonometry-basics -> SOLUTION: Consider the graph of y = tan x (a)How does it show that the tangent of 90 degrees is undefined? (b)What are other undefined x values? (c)What is the value of the tangent of ang      Log On


   

Question 53917: Consider the graph of y = tan x
(a)How does it show that the tangent of 90 degrees is undefined?
(b)What are other undefined x values?
(c)What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)?
(d)How does the graph show this?
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Csin%28x%29%2Fcos%28x%29%29
90 degrees = pi/2 or about 1.5708
If you go that many digits on the x-axis, there is no point that is determined by the graphed line. This is either called inifinity or undefined.
Other undefined values: 3pi/2, 5pi/2, 7pi/2, -pi/2, -3pi/2, -5pi/2 there are an infinite amount of undefined values.
The undefined values can be given as: (where k is an integer)
pi/2 +- pik
If the value of a degree is a little below 90 degrees, then the tangent of that angle would be great! If the value of the degree is a little over 90 degrees, then the tangent of that angle would be extremely small (in the negatives.) The graph shows this easily. At pi/2, there is no point on the graphed line that results from tan(pi/2).
Just look at this piece:
graph%28300%2C300%2C-1.5708%2C1.5708%2C-10%2C10%2Csin%28x%29%2Fcos%28x%29%29
y ~> +infinity, x ~> +infinity
y ~> -infinity, x ~> -infinity
A little less than the undefined value of pi/2 shows us that y is high. Vise versa for a little more.