sinθ = O/H cosecθ = 1/sinθ cosθ = A/H secθ = 1/cosθ tanθ = O/A cotθ = 1/tan

Exact Ratios sinθ = cos(90° – θ)

45° √2 1 1 √3 45° 1 60° 30° 2

cosθ = sin(90° – θ) tanθ = cot(90° – θ) cosecθ = sec(90° – θ) secθ = cosec(90° – θ) cotθ = tan(90° – θ)

Bearings 1. True bearings – clockwise from north.

N

W 150°

E

S

2. Compass bearings – directed north to south

N N40° E 40° W E

1 knot = 1 nautical mile

S40° W S

Angles of Any Magnitude

S T

A C

90° - 180°

0° - 90°

270° - 180°

270° - 360°

Mathematics Summary Sheets – Trigonometry

1

All angles need to be described using their relationship to 0°, 180°, 360°.

180° - θ

0° - θ

Matching angles Quad 1 30° 45° 60° Quad 2 150° 135° 120° Quad 3 210° 225° 240° Quad 4 330° 315° 300°

180° + θ

360° - θ

Angles that are multiples of 90° Sin

1

cos

0

tan

∞

0

0

0

-1

1

0

-1

0

∞

Domain: describes all the values of that ‘x’ is able to take. Range: describes all the values that ‘y’ is able to take. Period: of a graph describes the part of a graph, which is periodically repeated. It uses the horizontal scale. Amplitude: of a ‘wave’ graph is the height of the wave fro the horizontal.

Relations Between the Trig Ratios sin θ = y tan θ = y/x Pythagorean Identities 1. tan θ = sin θ /cos θ 2. cot θ = cos θ /sin θ 3. cos² θ + sin² θ = 1 4. 1 + tan² θ = sec² θ 5. cot² θ + 1 = cosec² θ cos θ = x cot θ = x/y

Mathematics Summary Sheets – Trigonometry

2

Trig Equations We need: • • Domain: sinx cosx all real x all real x

Range: –1 ≤ sinx ≤ 1 -1 ≤ cosx ≤ 1 ∞ < tanx < ∞

• • • •

tanθ exists except for θ = ± 90°, ± 270°, ± 450° … ASTC results Special triangles (exact ratios) Results for 0°, 90°, 180°, 270°, 360°. B c A a C

Area of a triangle

A= ½absinC

Sine Rule a b c ______ = ______ = ______ sinA sinB sinC

b

Cosine Rule b² + c² – a² 2bc

a² = b² + c² – 2bc cosA

or

cosA =...

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