Graphing Question For Trig

Question

Which of the following points is not on the graph of y= cot x?

A. (5pi/6, -sqrt(3))

B. (7pi/4, -1)

C. (4pi/3, sqrt(3))

Answer 1

Cotangent is the reciprocal function of tangent. The identity for tangent is sin/cosine. Therefore the identity for cotangent is cosine/sine. To determine if a point falls on a given graph, you are looking for what makes the statement true when you plug in a value for x. For example:

the first point is (5π/6, -√3)

1. plug in the x-value (5π/6) into x in cos(x)/sin(x). Cos(5π/6)= -√3/2. Sin(5π/6)= 1/2.
2. divide cosine by sine to check the y-value. (-√3/2) / (1/2) = -√3 which is the y-value of the given coordinate. So that statement is true and the point is on the graph.

the second point is (7π/4, -1)

1. plug in the x-value (7π/4). Cos(7π/4)= √2/2. Sin(7π/4)= -√2/2.
2. divide cosine by sine to check the y-value. (√2/2) / (-√2/2) = -1. So that statement is true and that point is also on the graph.

the third point (4π/3, √3)

1. plug in the x-value (4π/3). Cos(4π/3)= -1/2. Sin(4π/3)= -√3/2.
2. divide cosine by sine to check the y-value. (-1/2) / (-√3/2) = √3/3. That makes the statement false since that does not match the given y-value of the coordinate. Therefore, that point is NOT on the graph of y=cot(x).

This can also be checked on the calculator:

1. In Y=, type in y=1/tan(x)
2. Use zoom- trig (option 7 on most TI-graphing calculators)
3. Press 2nd, TRACE, value (option 1)
4. Type in the x-value of the given coordinate and check to see if the y-value on the screen matches the given coordinate’s y-value.

Answer 2

B is not on the graph. The point would be (3pi/4, -1) on the graph of cot(x).