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### Graph a Sine Function Using Amplitude

The sine function and any of its variations have two important characteristics: the amplitude and period of the curve. You can determine these characteristics by looking at either the graph of the function [more…]

### Adjusting the Period of a Sine Function

The period of a trigonometry function is the extent of input values it takes for the function to run through all the possible values and start all over again in the same place to repeat the process. In [more…]

### Understanding How a Sine Function Works

A general equation for the sine function is *y* = *A*sin *Bx*. The *A* and *B* are numbers that affect the amplitude and period of the basic sine function, respectively. [more…]

### Shift a Sine Function in a Graph

Playing around with the amplitude and period of the sine curve can result in some interesting changes to the basic curve on a graph. That curve is still recognizable, though. You can see the rolling, smooth [more…]

### Use the Sine to Show the Number of Daylight Hours in a Location

The graphs of sine curves and the cofunction, cosine, are useful for modeling situations that happen over and over again in a predictable fashion. Some examples include the weather, seasonal sales of goods [more…]

### Use Cosine to Show the Average Daily Temperature for a Location

You can use the graph for a trigonometry function to show average daily temperatures at a specific location. For example, a relatively reasonable model for the average daily temperature in Peoria, Illinois [more…]

### Use a Graph to Show Average Body Temperature over 24 Hours

You can use the graph of a trigonometry function to show temperature change over time. For example, the temperature of a person’s body fluctuates during the day instead of staying at a normal 98.6 degrees [more…]

### Use a Graph to Show the Change in Sales over a Year

You can use the graph of a trigonometry function to show sales amounts over a given period of time. Here’s an example: Even though people in many parts of the world play soccer year-round, certain times [more…]

### Graph Biorhythm Cycles

You can use the graph of a trigonometry function to plot your biorhythm cycles. Many years ago, the public showed great interest in a person’s *biorhythms* [more…]

### Graph Multiples of the Tangent Function

In trigonometry, tangent values go from negative infinity to positive infinity. So when you multiply the entire tangent function by a number, here’s what happens: If you multiply by a number bigger than [more…]

### Graph Tangent Functions with Variable Multipliers

In trigonometry, multiplying the angle variable in a tangent function has the same effect as it does with sine and cosine functions — it affects the period of the function. If the multiple is 2, as in [more…]

### Translating Tangent Functions on a Graph

Adding a number to a tangent function results in raising the curve on the graph by that amount. Likewise, subtracting a number drops the curve. [more…]

### Graph the Cosecant Function

One really efficient way of graphing the cosecant function is to first make a quick sketch of the sine function (its reciprocal). With the sine sketch in place, you can draw the asymptotes of the cosecant [more…]

### Shift a Cosecant Function on a Graph

The cosecant function is affected by the same multiplication, addition, and subtraction principles that affect the other functions. For example, adding or subtracting a number to or from the cosecant function [more…]

### Graph the Asymptotes of a Secant Function

To graph the secant curve, you first identify the asymptotes by determining where the reciprocal of secant — cosine — is equal to 0. Then you sketch in that reciprocal, so you can determine the turning [more…]

### Graph Variations on a Secant Function

The graph for a secant function is different from the cosecant in several ways, but one of the most obvious ways is that the graph of the secant is symmetric about the [more…]

### Graph Inverse Sine and Cosine Functions

The graphs of the inverse trig functions are relatively unique; for example, inverse sine and inverse cosine are rather abrupt and disjointed. These graphs are important because of their visual impact. [more…]

### Graph Inverse Tangent and Cotangent Functions

The graphs of the tangent and cotangent functions are quite interesting because they involve two horizontal asymptotes. The asymptotes help with the shapes of the curves and emphasize the fact that some [more…]

### Graph Inverse Secant and Cosecant Functions

The graphs of the inverse secant and inverse cosecant functions will take a little explaining. First, keep in mind that the secant and cosecant functions don’t have any output values [more…]

### Find the Mirror Image of a Trigonometry Function on a Graph

When you multiply a trig function by a negative number, all the output values are reversed in sign. The positive values become negative, and the negative values become positive. The effect that this operation [more…]

### Measure Tidal Change Using a Trigonometry Graph

You can use trigonometry to graph the changes in high and low tides for a particular location. Along the coast, the tides are of particular interest. They are affected by the gravitational pull of both [more…]

### Tracking a Deer Population over Time Using Trigonometry Functions

The graphs of trig functions can be useful for showing natural cycles over time, such as temperature and population change. The following graph shows the population of a herd of deer, starting at the first [more…]

### Graph the Movement of an Object on a Spring

The graph of a trigonometry function can be useful for showing a progression over time, such as in a model for the height of an object attached to a spring. The same pattern doesn’t occur over and over [more…]

### Comparing Cosine and Sine Functions in a Graph

The relationship between the cosine and sine graphs is that the cosine is the same as the sine — only it’s shifted to the left by 90 degrees, or π/2. The trigonometry equation that represents this relationship [more…]

### Graph the Asymptote of a Tangent Function

An *asymptote* is a line that helps give direction to a graph of a trigonometry function. This line isn’t part of the function’s graph; rather, it helps determine the shape of the curve by showing where [more…]