Introduction to Trigonometry — Questions & Answers

Sample questions from Introduction to Trigonometry

1. Q1. The value of sec 30° is:

   • A.√3/2
   • B.2/√3✓
   • C.2
   • D.1/2
   Solution

   B is correct: sec is the reciprocal of cos, and cos 30° = √3/2, so sec 30° = 2/√3. A gives cos 30° itself, not its reciprocal. C is sec 60°. D is cos 60°.

2. Q2. For an acute angle θ, if sin θ increases, cos θ generally:

   • A.decreases✓
   • B.increases equally
   • C.becomes negative
   • D.remains 1
   Solution

   For acute angles, sine and cosine vary oppositely over 0° to 90°.

3. Q3. If 4 tan A = 3, where A is acute, then (1 − tan²A) ÷ (1 + tan²A) equals

   • A.7/25✓
   • B.25/7
   • C.16/25
   • D.9/25
   Solution

   tan A = 3/4, so the value is (1 − 9/16)/(1 + 9/16) = (7/16)/(25/16) = 7/25.

4. Q4. If cos θ=8/17, tan θ is:

   • A.15/8✓
   • B.8/15
   • C.17/8
   • D.15/17
   Solution

   The perpendicular is 15, so tan θ=15/8.

5. Q5. In the given figure, ΔABC is right-angled at B with AB = 24 cm and BC = 7 cm. The value of sin A is

   • A.24/25
   • B.7/25✓
   • C.7/24
   • D.25/7
   Solution

   AC = √(24² + 7²) = 25 cm, and the side opposite ∠A is BC, so sin A = 7/25.

Other Class 10 Mathematics chapters