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Year 11 · Trigonometry

Trigonometric identities

Trig identities are always true: sin²θ + cos²θ = 1, tan θ = sin θ ÷ cos θ, sin θ = cos(90° − θ). Trig equations have several solutions in 0°–360°.

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How to do it

  1. Find the reference angle from the exact value.
  2. Use the CAST diagram to find which quadrants give the sign.
  3. Write all solutions in range.

Worked example

sin 23° is equal to which of these?
sin θ = cos(90° − θ), so sin 23° = cos 67°.
Answer: cos 67°

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Check the sign of the value to pick the quadrants.

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