#### Transcript of 4.5: Graphs of Tangent, Cotangent, Secant and Cosecant

**4.5: Graphs of Tangent, Cotangent, Secant, and Cosecant**

1. What is the analysis of the tangent function? what is its graph?

2. How is the cotangent function different and similar to the tangent function?

3. How do you expect secant and cosecant functions to behave?

4. How do you solve a trig equation algebraically?

5. How would you sum up the analyses of the six basic trig functions?

4.5 Examples

1. Describe the graph of the function in terms of a basic trig function. Locate asymptotes and graph two periods:

A. y = tan 2x

B. y = 2 cot 2x

Solve for x on the given interval:

2. sec x = 2,

[0, (pi)/2]

3. csc x = 1,

[2(pi), 5(pi)/2]

Use a calculator to solve for x on the given interval:

4. csc x = 2,

[0, 2(pi)]

5. A hot-air balloon over Albuquerque is being blown due east from point P and traveling at a constant height of 800 ft. The angle y is formed by the ground and the line of vision from P to the balloon. This angle changes as the balloon travels.

(a) Express the horizontal distance x as a function of the angle y.

(b) When the angle is (pi)/20, what is its horizontal distance from P.

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