Unit 3 Graphing Review

Let’s graph some trig functions!

Graph y = -2 sin x

x

y

Graph y = cos x - 2

x

y

Graph y = 3 csc x +1

x

y

Graph y = sec 2x

x

y

Graph y = 2tan x

x

y

Graph y = cot 2x + 1

x

y

Graph y = 2sin4(x-π/2)

x

y

N

N

Time to practice some applications.

1. The Bay of Fundy in eastern Canada is known for the highest tides in the world. The depth of the water, d, in meters is given by the function

d = 10 + 7.5 cos (.507t), where t is the number of hours after midnight.

At what time does low tide first occur?

How deep is the water at high tide?

1

Part 1: Graph function on calculator.

Answer: about 6.2 hours after midnight – or about 6:12 am

Part 2: Find maximum value of graph.

Find the minimum value (2nd calculate). Is your answer the x or y value?

Is your answer the x or y value?

Answer: 17.5 feet Did you need to use the calculator for this answer?

x

y

12

Write the equation.

y = a sin bx + c

What does the 3 represent?

y = a sin bx + 3

What is the amplitude?

y = 2 sin ½ x + 3

y = 2 sin bx + 3

How do you find b ?

24

2 4

2

41

2

bb

b

b

P = 4π

3. A building’s temperature, T, varies with time of day, t, during the course of 1 day as

follows: T = 6 sin t + 81The air-conditioning operates when T > 80.

Graph this function for 5 < t < 15 and determine how many hours the air-

conditioning is off in the building to the nearest hour.

3

After graphing the function, what else do you need to know?

How will you find out when the temperature is 80 degrees or above?

Intersection points are at approximately 6.1, 9.6, and 12.4 What does that tell us in terms of this problem?

Answer to problem?

The air conditioning will be off between the hours of 5 and 6.1 and also between the hours of 9.6 and 12.4. The air conditioner is off for approximately 4 hours between times 5 and 15.

x

y

4

x

y

4

Period is 2π.

Range is 4 8y

x

y

Now let’s write some trig functions:

x

y

y = 3 sin x

x

y

y = cos x - 2

x

y

y = 4 cos 2x

x

y

y = - cos x

x

y

y = cos (x - π)

x

y

y = cos 3x + 3

x

y

y = 2 sin ½ x

x

y

y = sin 8x

π/2

1

-1

x

y

y = -2sin(x- π/4)

x

y

y = 3 sin 2x + 1

x

y

y = ½ sin (x- π)

ππ/2