Question 2 of 18beginner🔧 ApplyNumerical2 marks

If sin A = 34\frac{3}{4}, calculate cos A and tan A.

Correct Answer

cos A = 7\sqrt{7}/4 and tan A = 3/7\sqrt{7}

Exercise: EXERCISE 8.1 | Q: 3 | (Page Page 9)
For More Understanding

Explanation

This question tests the application of the fundamental trigonometric identity sin²A + cos²A = 1. Students must first use this identity to find cos A, then apply the relationship tan A = sin A/cos A to find tan A. The context clearly establishes these formulas in Example 9 and the identities section.

Solution Steps

  1. Step 1: Using the identity sin²A + cos²A = 1, we get cos²A = 1 - sin²A

  2. Step 2: Substituting sin A = 3/4, we get cos²A = 1 - (3/4)² = 1 - 9/16 = 7/16

  3. Step 3: Therefore, cos A = 7/16\sqrt{7/16} = 7\sqrt{7}/4

  4. Step 4: Using tan A = sin A/cos A, we get tan A = (3/4)/(7\sqrt{7}/4) = 3/7\sqrt{7}

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