explorers’ club

Note to self:

I was cleaning out some old notebooks and file and found my old TI-83 Graphing Calculator from high school (circa 1994-ish).  Inside its slip cover I found some old sticky notes with my trig tricks and tips.

The trig triangle of choice:

This triangle will be referenced by most of the tips below.

Radians to Degrees and back again:

• radians = degrees * π / 180
• degress = radians * 180 / π

SOH CAH TOA

• sin ϴ = opposite / hypotenuse
• cos ϴ = adjacent / hypotenuse
• tan ϴ = opposite / adjacent

Subdivision of cirle in 30º increments:

• 30º = π / 6
• 60º = 2π / 6
• 90º = 3π / 6
• 120º = 4π / 6
• 150º = 5π / 6
• 180º = π
• 210º = 7π / 6
• 240º = 8π / 6
• 270º = 9π / 6
• 300º = 10π / 6
• 330º = 11π / 6
• 360º = 2π

Subdivision of cirle in 45º increments:

• 45º = π / 4
• 90º = 2π / 4
• 135º = 3π / 4
• 180º = π
• 225º = 5π / 4
• 270º = 6π / 4
• 315º = 7π / 4
• 360º = 2π

Cosine constants for common values:

• cos 0º = 1
• cos 30º = √3 / 2
• cos 45º = √2 / 2
• cos 60º = 1 / 2
• cos 90º = 0
• cos 180º = -1
• cos 270º = 0

Sine constants for common values:

• sin 0º = 0
• sin 30º = 1 / 2
• sin 45º = √2 / 2
• sin 60º = √3 / 2
• sin 90º = 1
• sin 180º = 0
• sin 270º = -1

Tangent constants for common values:

• tan 0º = 0
• tan 30º = √3 / 3
• tan 45º = 1
• tan 60º = √3
• tan 90º = ∞
• tan 180º = 0
• tan 270º = ∞

Secant constants for common values:

• sec 0º = 1
• sec 30º = 2√3 / 3
• sec 45º = √2
• sec 60º = 2
• sec 90º = ∞
• sec 180º = -1
• sec 270º = ∞

Cosecant constants for common values:

• sec 0º = ∞
• sec 30º = 2
• sec 45º = √2
• sec 60º = 2√3 / 3
• sec 90º = 1
• sec 180º = ∞
• sec 270º = -1

Cotangent constants for common values:

• sec 0º = ∞
• sec 30º = √3
• sec 45º = 1
• sec 60º = √3 / 3
• sec 90º = 0
• sec 180º = ∞
• sec 270º = 0

Law of Cosines:

• a² = b² + c² – 2bc * cos α
• b² = a² + c² – 2ac * cos β
• c² = a² + b² – 2ab * cos γ

….formulated to solve for the cosines:

• cos α = (b² + c² – a²) / 2bc
• cos β = (a² + c² – b²) / 2ac
• cos γ = (a² + b² – c²) / 2ab

Law of Sines:

Given a circle with a radius = r circumscribed around a triangle,

• sin α / a = 2r
• sin β / b = 2r
• sin γ / c = 2r

and the rest that I couldn’t make sense of:

Some inversions of the advanced stuff I never use:

• arcsec ϴ = arccos (1 / ϴ)
• arccsc ϴ = arcsin (1 / ϴ)

Some domain, range and quadrant stuff regarding f(x) = y:

• y = tan^-1 x:
  • Domain: all real numbers
  • Range: -π / 2 – π / 2
  • Quadrants: I, IV
• y = cot^-1 x:
  • Domain: all real numbers
  • Range: 0 – π
  • Quadrants: I, II
• y = sec^-1 x:
  • Domain: x ≥ 1, x ≤ -1
  • Range: 0 – π
  • Quadrants: I, II
• y = csc^-1 x:
  • Domain: x ≥ 1, x ≤ -1
  • Range: -π / 2 – π / 2
  • Quadrants: I, IV