When you're graphing trigonometric functions like sine, cosine, and tangent, it’s really easy to make some common mistakes. Here are a few that I’ve seen or even made myself:
Forgetting the Amplitude and Period: Always keep in mind that the amplitude for the function ( y = A \sin(Bx) ) is the absolute value of ( A ), which is written as ( |A| ). The period, which is how long it takes for the wave to repeat, is calculated by ( \frac{2\pi}{|B|} ).
Incorrectly Labeling Axes: Make sure you label the x-axis with the right angle measurements. Use values like ( 0 ), ( \frac{\pi}{2} ), ( \pi ), and so on, instead of just random numbers.
Neglecting to Plot Key Points: Don’t forget to mark important points on your graphs! Key points include the highest and lowest points (max and min) and where the graph crosses the x-axis (intercepts). They are super helpful!
Misunderstanding Phase Shift: It’s important not to mix up phase shifts with amplitude shifts. For the function ( y = \sin(B(x - C)) ), the phase shift, which shows how much the graph moves left or right, is simply ( C ).
By keeping these tips in mind, you'll create better graphs of trigonometric functions!
When you're graphing trigonometric functions like sine, cosine, and tangent, it’s really easy to make some common mistakes. Here are a few that I’ve seen or even made myself:
Forgetting the Amplitude and Period: Always keep in mind that the amplitude for the function ( y = A \sin(Bx) ) is the absolute value of ( A ), which is written as ( |A| ). The period, which is how long it takes for the wave to repeat, is calculated by ( \frac{2\pi}{|B|} ).
Incorrectly Labeling Axes: Make sure you label the x-axis with the right angle measurements. Use values like ( 0 ), ( \frac{\pi}{2} ), ( \pi ), and so on, instead of just random numbers.
Neglecting to Plot Key Points: Don’t forget to mark important points on your graphs! Key points include the highest and lowest points (max and min) and where the graph crosses the x-axis (intercepts). They are super helpful!
Misunderstanding Phase Shift: It’s important not to mix up phase shifts with amplitude shifts. For the function ( y = \sin(B(x - C)) ), the phase shift, which shows how much the graph moves left or right, is simply ( C ).
By keeping these tips in mind, you'll create better graphs of trigonometric functions!