Reciprocal Functions

Reciprocal Functions

Graph of y = cosec x

Properties of the Cosecant Curve

1. The period is 360^o or 2p.

2. The graph is symmetrical about the origin.

3. There are vertical asymptotes at x = -2p, -p, 0, p, 2p, etc.

4. There are turning points at (p/2, 1), (-p/2, -1), etc

5. The curve is not defined for the range -1 < y < 1.

6. The curve is not continuous.

Graph of y = sec x

Properties of the Secant Curve

1. The period is 360^o or 2p.

2. The graph is symmetrical about the y-axis.

3. There are vertical asymptotes at x = -p/2, p/2, 3p/2, etc

4. There are turning points at (-p,-1), (0, 1), (p, 1), etc

5. The curve is not defined for the range -1 < y < 1.

6. The curve is not continuous.

Graph of y = cot x

Properties of Cotangent Curve

1. The period is 180^o or p.

2. The range is all real numbers.

3. The graph is symmetrical about the origin.

4. The curve is not continuous. There are vertical asymptotes at x = 0^o, 180^o,...