- Education
- Math
- Trigonometry
- How to Recognize Basic Trig Graphs

# How to Recognize Basic Trig Graphs

*6*

## The graph of *y* = sin* x*.

The graph of the sine function is a nice, continuous wave that rolls along gently and keeps repeating itself. The domain, or *x-*values, of the sine function includes all angles in degrees or all real numbers in radians, so the curve has no breaks or holes.

*6*

## The graph of *y* = cos* x*.

The relationship between the sine and cosine graphs is that the cosine is the same as the sine shifted to the left by 90 degrees.

*6*

## The graph of *y* = tan *x*.

The tangent function can be written as the ratio of the sine divided by the cosine.

*6*

## The graph of *y* = cot *x*.

The graphs of the tangent function lay the groundwork for the graphs of the cotangent. After all, they’re cofunctions and reciprocals, and have all sorts of connections.

*6*

## The graph of *y* = sec *x*.

The techniques that you use to graph the secant curve parallel those that you use to graph the cosecant. First, identify the asymptotes by determining where the reciprocal of secant — cosine — is equal to 0. Then sketch in that reciprocal, and you can determine the turning points and general shape of the secant graph.

*6*

## The graph of *y* = csc *x*.

The cosecant function is the reciprocal of the sine function (meaning, the cosecant equals 1 divided by the sine).