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Year 11 · Trigonometry

Solve trigonometric equations

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

Solve tan θ = √3 for 0° ≤ θ < 360°.
The reference angle is 60°; tan is positive in the quadrants that give 60°, 240°.
Answer: 60°, 240°

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Check the sign of the value to pick the quadrants.

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