graph of y=tan(x)

TL;DR

Learn how to graph the function y=tan(x) by finding its domain, identifying vertical asymptotes, and understanding its shape.

Transcript

William this video is for you I'm going to show you how to graph y is equal to tangent X and I will do other examples on the graph of tangent of whatsoever for you as well anyways let's look at this one first we are going to find the domain of just tangent X and we have to know a few things first we know that tangent X is the same as sin x over cos... Read More

Key Insights

• ❣️ The domain of the tangent function y=tan(x) is restricted by the denominator, ensuring that the cosine x is not zero.
• 👈 Vertical asymptotes occur at x values of pi/2, 3pi/2, 5pi/2, etc., since cosine is zero at these points.
• 🤪 The graph of y=tan(x) goes infinitely up and down as it approaches and moves away from the vertical asymptotes.
• ♾️ The range of y=tan(x) is from negative infinity to positive infinity.
• 🤩 Key points on the graph include (0, 0) and (pi/4, 1).
• 🤨 The period of the graph is pi, and it repeats itself indefinitely.
• 🤪 The shape of the tangent graph approaches vertical asymptotes, resulting in a curve that goes straight up and down between the asymptotes.

Questions & Answers

Q: How do you find the domain of the tangent function?

To find the domain of y=tan(x), we need to ensure that the denominator, cosine x, is not zero. By using the unit circle, we can determine that the vertical asymptotes occur at x values of pi/2, 3pi/2, 5pi/2, etc.

Q: How do you graph the function y=tan(x)?

To graph y=tan(x), start by plotting the x values on the x-axis, including the vertical asymptotes. Remember that the shape of the graph approaches the vertical asymptotes. You can also identify key points like (0, 0) and (pi/4, 1) to help sketch the curve.

Q: What is the range of the tangent function?

The range of y=tan(x) is from negative infinity to positive infinity. This is because the graph goes infinitely down as it approaches the vertical asymptotes and infinitely up as it moves away from the asymptotes.

Q: How can I represent the domain of the tangent function using set-builder notation?

The domain of y=tan(x) can be represented using set-builder notation as follows: X is not equal to k*pi/2, where k is any odd integer.

Summary & Key Takeaways

• The video teaches how to find the domain of the tangent function, which requires ensuring that the denominator (cosine x) is not zero.

• Using the unit circle, the values for x where cosine is zero (vertical asymptotes) are determined, such as pi/2, 3pi/2, 5pi/2, etc.

• The graph of y=tan(x) is drawn by plotting the values on the x-axis and incorporating the vertical asymptotes. The key features of the graph, such as zero points and shape, are explained.