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Math 240 Class Packet #1

Topics

- What is an angle? What is a degree? - Vocabulary associated with angles (Right, Straight, Acute, Obtuse, Complementary, Supplementary) - Vocabulary associated with triangles (Equilateral, Isosceles, Scalene, Acute, Obtuse, Right) - The Pythagorean theorem and derivations for 30/60/90 and 45/45/90 triangles

First Things First

1) Consider an angle α = 47°.

a) About what fraction of one full rotation does this represent?

b) Classify this angle as Right, Straight, Acute, or Obtuse.

c) Find the complement and supplement for this angle (if they exist).

2) Let α = 25°, β = 35°, γ = 120°.

a) Identify all applicable terms for the triangle: Equilateral, Isosceles, Scalene, Acute, Obtuse, Right.

b) If A, B, andC are the lengths of the sides opposite each of the given angles, order them from largest to smallest.

3) Use the Pythagorean theorem to fill in the rest of the table given below.

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4) Use your result from (3) to find the lengths of all sides in a 30/60/90 triangle where the side opposite of the 60° angle is 5.

5) For the figure shown below, use what you know about triangles to determine how many feet of material will be needed to make the tent.

Do it Yourself

6) Consider an angle β = 110°.

a) About what fraction of one full rotation does this represent?

b) Classify this angle as Right, Straight, Acute, or Obtuse.

c) Find the complement and supplement for this angle (if they exist).

7) Let α = 88°, β = 22°, γ = ?°.

a) Identify all applicable terms for the triangle: Equilateral, Isosceles, Scalene, Acute, Obtuse, Right.

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b) If A, B, andC are the lengths of the sides opposite each of the given angles, order them from largest to smallest.

8) Use the Pythagorean theorem to fill in the rest of the table given below.

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9) Use your result from (4) to find the lengths of all sides in a 45/45/90 triangle where the side opposite of the 90° angle is 10.

10) Find r if AB = 8andAD = 12. (Hint: Think about solving (8 + r)2 = r2 + 122)

Class Packet #1.nb ���3

Math 240 Class Packet #2

Topics

- Defining trig functions as the ratios of the (x, y) coordinates on the terminal side of θ. - Using given ratios to evaluate other trig functions.

First Things First

1) Use the definitions of the six trigonometric functions to complete the table given below.

���� �������� ��� θ ��� θ ��� θ ��� θ ��� θ ��� θ �������� ����� ���� ������

2) Find the values for all six trig functions of θ if the given point lies on the terminal side of the angle.

a) (-3, -4)

b) 2 , 2

3) Check off all possible quadrants that θ could terminate in based on the given information.

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��� θ = �

�

��� θ = -�

��

��� θ = -��

��

4) Find each of the remaining trig functions given the information below.

i) sinθ = 12 13

terminating in Q1

ii) tanθ = 3 4 terminating in Q3

Do it Yourself

5) Identify the sign for each of the given trig functions in the given quadrant.

�� �� �� �� ��� θ ��� θ ��� θ ��� θ ��� θ ��� θ

6) Find the values for all six trig functions of θ if the given point lies on the terminal side of the angle.

a) 3 , -1

b) (-1, -2)

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7) Check off all possible quadrants that θ could terminate in based on the given information.

�� �� �� ��

��� θ = -�

�

��� θ = �

�

��� θ = ��

��

8) Find each of the remaining trig functions given the information below.

i) cosθ = -12 13

terminating in Q2

ii) sinθ = 3 4 terminating in Q1

Class Packet #2.nb ���3