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Solving simple trig equations

Level 9 · Trigonometry · for questions like “Solve 2 sin x = 1 for x from 0° to 360°.”

💡 The idea

Get sin x (or cos x, or tan x) on its own, find one angle from the special values, then find the second angle in the other quadrant with the same sign.

The unit circle with a 150 degree angle

🪜 The steps

  1. Rearrange: 2 sin x = 1, so sin x = 1/2.
  2. First angle: 30°.
  3. Second angle: sin is also positive in quadrant II, at 180° − 30° = 150°.

✏️ Worked examples

1. 2 sin x = 1: 30° and 150°.

2. 2 cos x = 1: cos x = 1/2, so 60°. Cos is also positive in quadrant IV: 60° and 300°.

3. tan x = 1: 45°, and tan is positive in quadrant III too: 45° and 225°.

🎯 Try these

  1. 2 cos x = −1
  2. √2 sin x = 1
  3. tan x = √3

Answers: 1) 120° and 240° 2) 45° and 135° 3) 60° and 240°

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