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Maths
Summary
Trigonometric graphs are a class of "wave" graphs. They repeat themselves after a point, which makes them periodic. There are three main trigonometric graphs: sine, cosine and tangent and there are key points on each to learn.
The graph of is pictured above. The -axis displays degrees, the unit of angle. You can see that the graph passes through the origin and has peaks where and throughs where . The -coordinates are evenly spaced out such that the peaks are a horizontal distance of from each other and the troughs also have the same gap between them. The curve goes on forever in the positive and negative -directions but never goes higher than nor lower than .
The key points you need to know are the coordinates of the peaks, troughs and the -intercepts. It repeats itself every on the -axis.
The graph of is very similar to the sine graph above, but is shifted horizontally by units (when the -axis is in degrees). Hence the cosine graph (often referred to as the "cos" graph) intersects the -axis at . Like the sine graph, the cosine graph repeats itself every degrees on the -axis.
Give the coordinates of two points where intersects the -axis.
Reading off the graph, you can see that two examples of -intercepts are and .
Note: The cosine graph is mirrored in the -axis.
The graph of is different to the other two trigonometric graphs shown here in that it has a different shape and it repeats itself every degrees rather than just every degrees. You still need to know key points on it: it passes through the -axis at the origin and again every degrees in the positive and negative -directions.
At (and also at every jump of ), there is what is called an asymptote. This is a point on a curve where it gets closer and closer to a point, but never reaches it. So the graph of has no value when , but very close to , it has a -value that is very big in the positive direction (if ) or very big in the negative direction (if ).
Using a calculator, find and also .What happens if you type ?
Typing these into a scientific calculator gives
each to two decimal places. Typing gives a "math error" since there is no value for this - the graph never reaches . Another way of thinking of this is that coming from the left, gets bigger as it approaches . It shoots off infinitely. But coming from the right, it shoots off to negative infinity. Since cannot be infinity, nor negative infinity (and especially not both), it does not have a value.
FAQs
Question: What is an asymptote?
Answer: This is a point on a curve where it gets closer and closer to a point, but never reaches it.
Question: How often do the sine and cosine graphs repeat themselves?
Answer: They repeats themselves every 360 degrees on the x-axis.
Question: What are the three key trigonometric graphs?
Answer: y=sin(x), y=cos(x) and y=tan(x).
Theory
Exercises
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