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Year 11 · Trigonometry

Exact trigonometric values

Some angles have exact trig values you can find from two special triangles, and radians measure angles with π.

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How to do it

  1. 45° triangle: sides 1, 1, √2. 30°–60° triangle: 1, √3, 2.
  2. Read sin, cos, tan straight off the triangle.
  3. 180° = π radians: multiply degrees by π/180.

Worked example

What is the exact value of cos 90°?
Use the special triangles: a 45° triangle has sides 1, 1, √2 and a 30°–60° triangle has sides 1, √3, 2. cos 90° = 0.
Answer: 0

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Watch out
cos 60° is also 1/2, but sin 60° is √3/2.

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