Lesson 9E More Hidden Identities Practice Understanding

Ready

In the diagram, complex numbers have been graphed as vectors. Rewrite each complex number as a point in the form .

-3 4i, 5 2i, and 1-6i graphed as vectors. real axis–5–5–5555imaginary axis–5–5–5555000

1.

graphs as

2.

graphs as

3.

graphs as

4.

Graph the complex numbers as vectors on the diagram.

-3 4i, 5 2i, and 1-6i graphed as vectors. real axis–5–5–5555imaginary axis–5–5–5555000

5.

The magnitude of a complex is its modulus. It is symbolized by the notation where .

Find the modulus of each of the complex numbers.

a.

b.

c.

d.

e.

f.

g.

Set

Solve the following trigonometric equations. Write your answer(s) in the form ( , where represents the interval between successive solutions and is any integer. Note: sometimes the next solution can be described as just or some other interval, instead of .)

6.

7.

8.

9.

10.

11.

12.

13.

14.

Go

Use the graph to find all of the values for when , for the given equation. Write your answer(s) in the form , where represents the interval between successive solutions.

15.

Graph of y=sinx 1 x–2–2–2–1–1–1111222333444y111222000

16.

Use the unit circle to explain the solutions you found in problem 15.

Unit circle with points A(1,0), (0,1), F(-1,0), and (0,-1). (0,-1)A(-1,0)(0,1)(1,0)F

17.

Use the graph to approximate the points of intersection of the graphs of and .

graph of y1=2sinx 1 and y2=1/3x 2 x–3π / 2–3π / 2–3π / 2–π–π–π–π / 2–π / 2–π / 2π / 2π / 2π / 2πππ3π / 23π / 23π / 2y–1–1–1111222333000

18.

The scale on the -axis in the graph of problem 18 is . The scale in the graph of problem 20 is . Yet the units on both axes is radians.

a.

Label the graph with the approximate location of and .

Graph of y=sinx 1 x–2–2–2–1–1–1111222333444y111222000

b.

Label the graph with the approximate location of , , , and .

graph of y1=2sinx 1 and y2=1/3x 2 x–3π / 2–3π / 2–3π / 2–π–π–π–π / 2–π / 2–π / 2π / 2π / 2π / 2πππ3π / 23π / 23π / 2y–1–1–1111222333000