Trigonometric Fundamentals Flashcards
1
Q
Primary Trigonometric Ratios
A
- sin θ = y/r
- cos θ = x/r
- tan θ = y/x = sin θ/cos θ
2
Q
Sides of a triangle
A
- O: Opposite (y)
- A: Adjacent (x)
- H: Hypotenuse (r)
3
Q
Finding the Angle
A
- sin⁻¹ y/r
- cos⁻¹ x/r
- tan⁻¹ y/x
- = θ
4
Q
Reciprocal Trigonometric Ratios
A
- csc θ = 1/sin
- sec θ = 1/cos
- cot θ = 1/tan
5
Q
Negative Angles and Trigonometric Ratios
A
- sin(-θ) = -sin θ
- cos (-θ) = cos θ
- tan (-θ) = - tan θ
6
Q
Special Angle: 45°
A
- x = 1
- y = 1
- r = √2
7
Q
Special Angle: 30°
A
- x = √3
- y = 1
- r = 2
8
Q
Special Angle: 60°
A
- x = 1
- y = √3
- r = 2
9
Q
Special Angle: 0°
A
- x = 1
- y = 0
- r = 1
10
Q
Special Angle: 90°
A
- x = 0
- y = 1
- r = 1
11
Q
Special Angle: 180°
A
- x = -1
- y = 0
- r = 1
12
Q
Properties of QI
A
- Top-right quadrant
- All positive values
13
Q
Properties of QIl
A
- Top-left quadrant
- Positive sin values
14
Q
Properties of QIll
A
- Bottom-left quadrant
- Positive tan values
15
Q
Properties of QIV
A
- Bottom-right quadrant
- Positive cos values
16
Q
Coterminal Angles
A
- a = b + k360°, k ∈ N
- Where a, b are coterminal angles
17
Q
Negative Angles
A
- m = n + 360°
- Where m is positive and n is negative
18
Q
Related Acute Angles
A
- β = α - 90(k - 1)
- β is the related acute angle
- α is the principle angle
- k is the quadrant
19
Q
Sine Law
A
- Sin A/a = Sin B/b = Sine C/c
- Area = ab Sin C/c
20
Q
Cosine Law
A
- a² = b² + c² - 2bc(cos A)
- Cos A = (b² + c² - a²)/2bc
21
Q
One Solution (Ambiguous Case)
A
- a > b, A > 90° OR
- a ≥ b, A ∈ (0°, 90°]
22
Q
No Solution (Ambiguous Case)
A
a < b, A ∈ (0°, 90°] AND a < h
23
Q
Two Solutions (Ambiguous Case)
A
a < b, A ∈ (0°, 90°] AND a > h
24
Q
Bearing Value
A
- a = 90 - b
- a is the standard form angle
- b is the bearing form angle
