Unit 11A - Trigonometry

Question 1

How do you determine which sides are opposite, adjacent or the hypotenuse relative to an angle? (3)

Answer 1

1. Hypotenuse - Opposite Right Angle
2. Adjacent - Next to Angle
3. Opposite - Only Side that Doesn’t Touch

Question 2

Definition of Sine (2)

Answer 2

1. sinθ (ratio)
2. Opposite/Hypotenuse

Question 3

Definition of Cosine (2)

Answer 3

1. cosθ (ratio)
2. Adjacent/Hypotenuse

Question 4

Definition of Tangent (2)

Answer 4

1. tanθ (ratio)
2. Opposite/Adjacent

Question 5

What is an abbreviated to remember the ratios of Sine, Cosine & Tangent?

Answer 5

SOH - CAH - TOA (ONLY APPLIES TO RIGHT TRIANGLES)

Question 6

How do you find an side and angle measure based on cosine, sine and tangent? (3)

Answer 6

1. Because tan, sine & cosine are considered numbers
2. You can make a proportion by adding a denominator of 1
3. For angle measure, multiply inverse (sin -1) by ratio

Question 7

How many degrees is π equivalent to?

Answer 7

180 = π radians

Question 8

How do you convert degrees to radians?

Answer 8

multiply π/180

Question 9

How do you convert radians to degrees?

Answer 9

1. Substitute π for 180 degrees
2. multiply 180/π

Question 10

Definition of Angle of Elevation & Angle of Depression (4)

Answer 10

• Angle between horizontal & line of sight
• Angle of Elevation (above)
• Angle of Depression (below)
• Angles are congruent bc horizontal lines are parallel & alt. int. angles congruent

Question 11

How do you draw a horizontal line for angle of depression or angle of elevation? (3)

Answer 11

1. Draw horizontal line from eye level of the person
2. Draw a line upwards or downwards based on what they’re looking at
3. When not given the height of person from “eye level”, draw horizontal from their feet

Question 12

What is an instinct you must utilize when given radians for angle measure in a word problem?

Answer 12

Convert to Degrees

Question 13

What is the reciprocal of Sine? (3)

Answer 13

1. Cosecant
2. csc (x)
3. Hypotenuse/Opposite

Question 14

What is the reciprocal of Cosine? (3)

Answer 14

1. Secant
2. sec (x)
3. Hypotenuse/Adjacent

Question 15

What is the reciprocal of Tangent? (3)

Answer 15

1. Cotangent
2. cot (x)
3. Adjacent/Opposite

Question 16

How do you find the ratios of csc (72), sec (72) and cot (72) in a calculator)? (3)

Answer 16

1. csc (72) - 1/sin (72)
2. sec (72) - 1/cosin (72)
3. cot (72) - 1/tangent (72)

Question 17

How do you find the measure of an angle of csc (x), sec (x) and cot (x)?

Answer 17

Convert the functions to their reciprocal functions (sin, cosin & tan) then solve!

Question 18

What are Cofunctions? (5)

Answer 18

1. Pairs of Trigonometric Functions
2. Congruent when their angles are complementary
3. Sine & Cosine
4. Tangent & Cotangent
5. Secant & Cosecant

Question 19

What are the rules when it comes to cofunctions? (2)

Answer 19

1. If Cofunctions of two angles are congruent, then the angles are complementary
2. If two angles are complementary, then their cofunctions are congruent

Question 20

What is the Pythagorean Identity? (3)

Answer 20

1. sin²θ + cosin²θ = 1
2. sin²θ = 1 - cos²θ
3. cos²θ = 1 - sin²θ

Question 21

What is the formula for tangent in trig identities?

Answer 21

tanθ = sinθ/cosθ

Question 22

What is the formula for cotangent in trig identites?

Answer 22

cotθ = cosθ/sinθ

Question 23

How do you simplify Trig Expressions? (5)

Answer 23

1. Rewrite each expression in terms of sinθ and cosθ
2. sin²θ + cosin²θ = 1, cscθ = 1/sinθ, secθ = 1/cosθ
3. Put sinθ and cosθ over 1
4. If division is involved, rewrite expression horizontally
5. Utilize the Keep, Change, Flip!

Question 24

What acronym helps you find the difference between the Trig Expressions Formulas for tangent and cotangent?

Answer 24

Tanning in South Carolina