Unit 11B - Trigonometry

Question 1

What are the reference angles? (3)

Answer 1

1. Acute angle formed
2. By terminal side & x - axis
3. How far away are you from the x- axis?

Question 2

Definition of Standard Position

Answer 2

An angle is in standard position when its initial side is on the positive x - axis

Question 3

Definition of Initial Side (2)

Answer 3

1. Doesn’t move
2. Is on positive x - axis in standard position

Question 4

Definition of Terminal Side (2)

Answer 4

1. Moves as the angle measure changes
2. Determines the quadrant where the angle is

Question 5

What are the quadrantal angles?

Answer 5

1. 0°
2. 90°
3. 180°
4. 270°
5. 360°
6. 450°

Question 6

Definition of Unit Circle

Answer 6

Definition: Circle with radius of 1 and centered at the origin
Functions: Cos𝜃 = X, Sin𝜃 = Y, Tan𝜃 = Y/X
Coordinates: 0° & 360° = (1,0), 90° = (0,1), 180° = (-1, 0), 270° = (0, -1)

Question 7

Definition of ASTC Chart?

Answer 7

Tells you which function is positive in that quadrant

Question 7

What is the acronym to remember the order of ASTC?

Answer 7

All Students Take Classes

Question 8

What is something to keep in mind about reciprocal functions in ASTC?

Answer 8

Reciprocal functions hold the same sign value as original functions

Question 8

In right triangle ABC, angle A = 90.
If b = 3.64 and a = 7.28, find angle b.
What does a & b mean in the context of the problem?

Answer 8

a & b are sides of the triangle.
a is the side opposite of angle a
b is the side opposite of angle b

Question 9

What is QRS?

Answer 9

Quadrant
Reference Angle
Sign (+ or -)

(Used to find exact values of functions & their angles)

Question 10

What is the law of sines? (3)

Answer 10

1. a/sinA = b/sinB
2. Applies to all triangles (not only right)
3. Use Opposites - Opp. of sinA will be side a (a/sinA)

(Must be Given 2 angles & 1 Side or 2 Sides & 1 angle)

Question 11

What is the law of cosines? (4)

Answer 11

1. 𝑐2=𝑎2 + 𝑏2 − 2𝑎𝑏 ⋅ cos(C)
2. Both ends of the equation must always have the matching side & ∠
3. Use if there’s no angles given and no opposites
4. Look for SSS or SAS

(Must be Given 2 Sides & 1∠ or 3 Sides)

Question 12

What does it mean when you are solving a trig equation? How? (1/6)

Answer 12

1. Find the measure of an angle in a specified interval that makes the trig eq. true
2. Treat trig function as a variable
3. Solve equation
4. Find the reference angle using the exact value table
5. Instantly convert it to radians
6. Decide which quadrants angles could be using ASTC
7. Draw “Bow - Tie” and use Reference Angles to find Angle in Radians