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Tangent Graph
In this lesson, we will look at graphing the tangent function.
We will start with the unit circle.
A unit circle is a circle of radius one unit with its centre at the origin.
In the following diagram, the line l is a tangent to the unit circle at point P.
We can see that:
y = tan θ is known as the tangent function. Using the unit circle, we can plot the values of y against the corresponding values of θ.
The graph of y = tan θ, for 0˚ ≤ θ ≤ 360˚ obtained is as shown:
Properties of the tangent function:
The curve is not continuous. It breaks at θ = 90˚ and 270˚, where the function is undefined
tan θ= 0 when θ= 0˚, 180˚, 360˚. tan θ = 1 when θ= 45˚ and 225˚.
tan θ = –1 when θ= 135˚ and 315˚.
tan θdoes not have any maximum or minimum values. The range of values of tan θis –∞ < tan θ< ∞ .
As the point P moves round the circle in either the clockwise or anticlockwise direction, the tangent curve above repeats itself for every interval of 180˚. Its period is 180˚.
Example:
Sketch the graph of y = tan x for 0˚ ≤ x ≤ 360˚.
Solution:
Set up a table of values for y = tan x
x
0
45
90
135
180
225
270
315
360
tan x
0
1
undefined
–1
0
1
undefined
–1
0
Plot the points and join with a smooth curve.
Example:
The diagram shows a graph of y = tan x for0˚ ≤ x ≤ 360˚, determine the values of p, q and r.
Solution:
We know that for a tangent graph, tan θ = 1 when θ= 45˚ and 225˚. So, b = 45˚.
We know that for a tangent graph, tan θ = 0 when θ= 0˚, 180˚ and 360˚. So, c = 180˚.
Videos
Graphing the Tangent Function
Graphing the Tangent Function
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