Test Session Unit#6: Trigonometry (9th Mathematics)

MATHEMATICS EXAMINATION PAPER

Subject: Mathematics (SNC) – Trigonometry

Class: 9th

Unit: #6

Date: ______________

Time Allowed: ______________

Total Marks: ______________

Candidate Name:

Roll Number:

Marks Obtained:

Q1. Choose the correct option. (10 × 1 = 10 marks)

Q2. Write down short answers of following questions. (15 × 2 = 30 marks)

1. Find in which quadrant the following angle lies. Write a co-terminal angle for: \(65°\)

2. Find in which quadrant the following angle lies. Write a co-terminal angle for: \(135°\)

3. Find in which quadrant the following angle lies. Write a co-terminal angle for: \(-40°\)

4. Fill in the blank: \(\tan 30^\circ = \tan (90^\circ – 60^\circ) = \) ______

5. Fill in the blank: \(\tan 60^\circ = \tan (90^\circ – 30^\circ) = \) ______

6. Fill in the blank: \(\sin 60^\circ = \sin (90^\circ – 30^\circ) = \) ______

7. Fill in the blank: \(\cos 60^\circ = \cos (90^\circ – 30^\circ) = \) ______

8. Fill in the blank: \(\cos 45^\circ = \cos (90^\circ – 45^\circ) = \) ______

9. If \(\theta\) lies in first quadrant, find the remaining trigonometric ratio of \(\theta: \cot\theta = \sqrt{\frac{3}{2}}\)

10. Find the value without using calculator: \(\tan 60^\circ\)

11. Find the value without using calculator: \(\sec 60^\circ\)

12. Evaluate: \(2\sin 60^\circ \cos 60^\circ\)

13. Evaluate: \(\sin 60^\circ \cos 30^\circ – \cos 60^\circ \sin 30^\circ\)

14. Find the value of \(x, y\) and \(z\) from the right angled triangle with \(y = 4 \text{ cm}\):

15. Convert the angle from degrees to radians: \(255^\circ\) (answer in terms of \(\pi\))

Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 10 = 20 marks)

1. Prove the trigonometric identity:

\[ (\sec\theta – \tan\theta)^2 = \frac{1 – \sin\theta}{1 + \sin\theta} \]

2. Solve the triangle when \(m\angle B = 90^\circ\):

\[ m\angle A = 60^\circ, \quad c = 4 \text{ cm} \]

3. Ladder problem:

A ladder is placed against a wall such that the foot of the ladder is \(2 \text{ m}\) away from the wall. The length of the ladder is \(8 \text{ m}\). Find the height of the wall.