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Ratios of 0°, 30°, 45°, 60° and 90° sheet
3-mark answer frame

Evaluate (3 sin²60° + 2 cot²45° − cosec²30°)/(sec²45° + cos²0°).

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found To find the value of the given expression using standard values.
  2. 2 · Write the formula or theorem From the table: sin 60° = √3/2, cot 45° = 1, cosec 30° = 2, sec 45° = √2, cos 0° = 1.
  3. 3 · Square each value sin²60° = 3/4, cot²45° = 1, cosec²30° = 4, sec²45° = 2, cos²0° = 1.
  4. 4 · Work out the numerator 3 × 3/4 + 2 × 1 − 4 = 9/4 + 2 − 4 = 1/4.
  5. 5 · Work out the denominator 2 + 1 = 3.
  6. 6 · Divide (1/4) ÷ 3 = 1/12.
  7. 7 · Check and box the answer Recheck each square from the table, then box the value 1/12.

Scoring tip: Write every standard value on a separate line before you substitute. Most marks are lost by squaring wrongly, for example writing cosec²30° = 2.