Unit Test: Introduction to Trigonometry

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: When cos A = 4/5, the value for tan A is (1 Mark)
(a) 3/5
(b) 3/4
(c) 5/3
(d) 4/3
Q2: Which of the following is the the simplest value of cos² θsin θ + sin θ (1 Mark)
(a) cosec θ
(b) sec θ
(c) sinθ
(d) cosine θ

Q3: True/ False (1 Mark)
tan θ = sin θ / cos θ

Q4: True/ False (1 Mark)

The value of sin 30° is greater than the value of sin 60°.

Q5: True/ False (1 Mark)

The cosine of an angle is the ratio of the opposite side to the adjacent side in a right triangle.

Q6: Evaluate cos 60° sin 30° + sin 60° cos 30°1

Q7: Prove that : 2cos² θ - 1cos⁴ θ - 2sin² θ + 1sin⁴ θ = cot⁴ θ - tan⁴ θ (2 Marks)

Q8: If 7sin²θ + 3cos²θ = 4, then find the value of tan θ. (2 Marks)

Q9: When sec 4A = cosec (A - 20°), here 4A is an acute angle, find out the value of A. (3 Marks)

Q10: If 3x = sec θ and 9 x² - 1x² = tan θ, then find the value.(3 Marks)
Q11:  If ∠A and ∠B are the acute angles such that cos A = cos B, then show that ∠ A = ∠ B. (3 Marks)

Q12: In triangle ABC, right-angled at B, when tan A = 1/√3 find out the value : (5 marks)
(i) sin A cos C + cos A sin C
(ii) cos A cos C - sin A sin C

 Q13: In ∆ ABC, the right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (5 Marks)
(i) sin A, cos A
(ii) sin C, cos C

You can find the solutions of this Unit Test here: Unit Test (Solutions): Introduction to Trigonometry