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Trigonometry: Sine, Cosine, Tangent as multipliers
opposite = hypotenuse x sin
adjacent = hypotenuse x cos
opposite = adjacent x tan
Memory aid: “Opposite goes with SIN”
Sine, Cosine and Tangent are
functions. The angle is the input, the
output is the ratio of sides of a right
angled triangle.
Special triangles
30o  sin  12
y  x tan 
Inverse trigonometric functions
 y

R
x
  cos 1  
R
 y
  tan 1  
x
  sin 1 
Opposite
the angle
Adjacent the angle
Practical applications of trigonometry
Pythagorean triples
h = 10tan38o
= 7.81m
38o
10m
Use an angle measuring device, a tape
measure and tan to calculate heights that
may be difficult to measure directly
Mathematics topic handout: Trigonometry – Sine, Cosine, Tangent as multipliers Dr Andrew French. www.eclecticon.info PAGE 1
Trigonometry was used to determine the positions of geophones during a
seismic survey of a beach in New Zealand.
(Cambridge University Earth Sciences, 2001).
Mathematics topic handout: Trigonometry – Sine, Cosine, Tangent as multipliers Dr Andrew French. www.eclecticon.info PAGE 2