How do we recognize and graph trigonometric functions? Graphs of Other Trigonometric Functions Essential Questions How do we recognize and graph trigonometric functions? Holt McDougal Algebra 2 Holt Algebra 2

The tangent and cotangent functions can be graphed on the coordinate plane. The tangent function is undefined when θ = + n, where n is an integer. The cotangent function is undefined when θ = n. These values are excluded from the domain and are represented by vertical asymptotes on the graph. Because tangent and cotangent have no maximum or minimum values, amplitude is undefined. To graph tangent and cotangent, let the variable x represent the angle θ in standard position.

Graphing Tangent Functions Equation of a Tangent Function No Amplitude Period Complete Cycle

Graphing Tangent Functions Draw one cycle of the function’s graph. Period

Graphing Tangent Functions Draw one cycle of the function’s graph. Period

Graphing Tangent Functions Draw one cycle of the function’s graph. Period

Graphing Tangent Functions Draw one cycle of the function’s graph. Translation down 3 Period

Graphing Tangent Functions Draw one cycle of the function’s graph. Translation Left p/4 Period

Graphing Tangent Functions Draw one cycle of the function’s graph. Period Reflection over x-axis

Lesson 11.2 Practice A