Lesson 8E The Amazing Inverse Trig Function Race Solidify Understanding

Ready

Plot each number in the rectangular complex plane.

1.

a blank 17 by 17 grid

2.

a blank 17 by 17 grid

3.

a blank 17 by 17 grid

4.

a blank 17 by 17 grid

5.

Use the Pythagorean Theorem to find the modulus of each number in problems 1–4. (Recall that the modulus is the distance between the point and the point representing the number.)

a.

modulus of

b.

modulus of

c.

modulus of

d.

modulus of

6.

Multiply each complex number in problems 1–4 by its conjugate.

a.

Multiply by its conjugate.

b.

Multiply by its conjugate.

c.

Multiply by its conjugate.

d.

Multiply by its conjugate.

e.

Compare your answers to the ones you got in problem 5. What do you notice?

Set

Use the given information to find the missing angle .

Round answers to the thousandths place ( decimal places).

7.

;

8.

;

9.

Explain why the answers to problems 7 and 8 are different even though the calculator gives you the same answer for both problems. (Include information about the meaning of the inverse trig function and the quadrant in which the terminal ray resides.)

10.

;

11.

;

12.

Explain why the answers to problems 10 and 11 are different even though the calculator gives you the same answer for both problems. (Include information about the meaning of the inverse trig function and the quadrant in which the terminal ray resides.)

13.

;

14.

;

15.

Explain why the answers to problems 13 and 14 are different even though the calculator gives you the same answer for both problems. (Include information about the meaning of the inverse trig function and the quadrant in which the terminal ray resides.)

16.

17.

Explain why problem 16 needed only one clue to determine a unique value for , while the other problems required at least two clues.

Fill in the indicated information for each of the inverse functions.

18.

a.

Graph .

a blank coordinate plane x–2–2–2222y–π–π–ππππ000

b.

domain:

c.

range:

19.

a.

Graph .

a blank coordinate plane x–2–2–2222y–π–π–ππππ000

b.

domain:

c.

range:

20.

a.

Graph .

a blank coordinate plane x–4–4–4–2–2–2222444y–π–π–ππππ000

b.

domain:

c.

range:

Go

Plot the given point in the polar coordinate system.

21.

a blank polar coordinate graph

22.

a blank polar coordinate graph

23.

a blank polar coordinate graph

24.

a blank polar coordinate graph

25.

a blank polar coordinate graph

26.

a blank polar coordinate graph