Objectives:- Find the period of the tangent function- Graph the tangent function- Solve tangent equations with a graphing calculator

PG 425

What is ? Let's look at our unit circle & thinkabout SOH CAH TOA.

sin x cos x

r =1

To make the graph of the basic tangent curve, we first make a table of angles & cosine values from the unit circle....

(angle)tan

(angle)tan tan ....now let's make our graph.

How does this compare to the graph in our "Solve It"?What is the period?

More Practice: Sketch 2 cycles of the following graphs: (on homework do 2 cycles)

a) 𝑦𝑦 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝜃𝜃 b) 𝑦𝑦 = tan −𝜃𝜃2

c) 𝑦𝑦 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝜃𝜃

Another way to solve:Type tan(degrees or radians into calculator)-100tan(16)=28.7 feet

Extra PracticeWhat is the value of the function at 30° and at 2𝜋𝜋

3radians?

a)𝑦𝑦 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝜃𝜃

b) 𝑦𝑦 = 50𝑡𝑡𝑡𝑡𝑡𝑡𝜃𝜃

Extra Practice

Solve each equation in the interval from 0 𝑡𝑡𝑡𝑡 𝑡𝜋𝜋. Round your answers to the nearest hundredth.

a)𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 3 b)𝑡𝑡𝑡𝑡𝑡𝑡𝜃𝜃 = −3 c) 6𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 4

Assignment:

Section 6.6: problems 1-10 (Sketch graph on #3), 14-18, 20

(on #14-16, graph 2 periods)