To understand what tangent functions look like on a graph, we need to break down their main features. The tangent function can be written as ( y = \tan(x) ).
Repeating Pattern (Periodicity):
The tangent function has a repeating pattern that happens every ( \pi ). This means that if you look at the values, they start over after every ( \pi ) radians.
For example, at ( y = \tan(0) ), it equals 0.
At ( y = \tan(\pi) ), it’s also 0.
Each full cycle goes from negative to positive values.
Asymptotes:
One special thing about the tangent function is its vertical asymptotes.
These are the places where the function doesn't have a value.
You find them at ( \frac{\pi}{2} + k\pi ), where ( k ) can be any whole number.
For example, at ( x = \frac{\pi}{2} ), there's a gap in the graph.
Key Points:
The graph of the tangent function passes through important points, including:
When you want to draw the tangent graph, start by marking the asymptotes and the key points.
The graph will go from really high to really low at these asymptotes, creating a wave-like pattern that makes the tangent function stand out.
By learning these features and how to graph them, you'll gain a better understanding of how tangent functions work. This will also help you get a stronger grasp of trigonometry!
To understand what tangent functions look like on a graph, we need to break down their main features. The tangent function can be written as ( y = \tan(x) ).
Repeating Pattern (Periodicity):
The tangent function has a repeating pattern that happens every ( \pi ). This means that if you look at the values, they start over after every ( \pi ) radians.
For example, at ( y = \tan(0) ), it equals 0.
At ( y = \tan(\pi) ), it’s also 0.
Each full cycle goes from negative to positive values.
Asymptotes:
One special thing about the tangent function is its vertical asymptotes.
These are the places where the function doesn't have a value.
You find them at ( \frac{\pi}{2} + k\pi ), where ( k ) can be any whole number.
For example, at ( x = \frac{\pi}{2} ), there's a gap in the graph.
Key Points:
The graph of the tangent function passes through important points, including:
When you want to draw the tangent graph, start by marking the asymptotes and the key points.
The graph will go from really high to really low at these asymptotes, creating a wave-like pattern that makes the tangent function stand out.
By learning these features and how to graph them, you'll gain a better understanding of how tangent functions work. This will also help you get a stronger grasp of trigonometry!