Trigonometric Fundamentals Flashcards by Eshan Kiritharan | Brainscape

Q

Primary Trigonometric Ratios

A

sin θ = y/r
cos θ = x/r
tan θ = y/x = sin θ/cos θ

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Q

Sides of a triangle

A

O: Opposite (y)
A: Adjacent (x)
H: Hypotenuse (r)

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Q

Finding the Angle

A

sin⁻¹ y/r
cos⁻¹ x/r
tan⁻¹ y/x
= θ

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Q

Reciprocal Trigonometric Ratios

A

csc θ = 1/sin
sec θ = 1/cos
cot θ = 1/tan

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Q

Negative Angles and Trigonometric Ratios

A

sin(-θ) = -sin θ
cos (-θ) = cos θ
tan (-θ) = - tan θ

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Q

Special Angle: 45°

A

x = 1
y = 1
r = √2

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Q

Special Angle: 30°

A

x = √3
y = 1
r = 2

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Q

Special Angle: 60°

A

x = 1
y = √3
r = 2

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Q

Special Angle: 0°

A

x = 1
y = 0
r = 1

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Q

Special Angle: 90°

A

x = 0
y = 1
r = 1

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Q

Special Angle: 180°

A

x = -1
y = 0
r = 1

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Q

Properties of QI

A

Top-right quadrant
All positive values

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Q

Properties of QIl

A

Top-left quadrant
Positive sin values

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Q

Properties of QIll

A

Bottom-left quadrant
Positive tan values

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Q

Properties of QIV

A

Bottom-right quadrant
Positive cos values

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Q

Coterminal Angles

A

a = b + k360°, k ∈ N
Where a, b are coterminal angles

Q

Negative Angles

A

m = n + 360°
Where m is positive and n is negative

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

Q

Sine Law

A

Sin A/a = Sin B/b = Sine C/c
Area = ab Sin C/c

Q

Cosine Law

A

a² = b² + c² - 2bc(cos A)
Cos A = (b² + c² - a²)/2bc

Q

One Solution (Ambiguous Case)

A

a > b, A > 90° OR
a ≥ b, A ∈ (0°, 90°]

Q

No Solution (Ambiguous Case)

A

a < b, A ∈ (0°, 90°] AND a < h

Q

Two Solutions (Ambiguous Case)

A

a < b, A ∈ (0°, 90°] AND a > h

Q

Bearing Value

A

a = 90 - b
a is the standard form angle
b is the bearing form angle