Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Unit Test: Introduction to Trigonometry
Unit Test: Introduction to Trigonometry | Mathematics (Maths) Class 10 PDF Download
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
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FAQs on Unit Test: Introduction to Trigonometry - Mathematics (Maths) Class 10
| 1. What are the basic trigonometric ratios and how are they defined? |  |
Ans. The basic trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They are defined based on a right triangle:
- Sine is the ratio of the length of the opposite side to the length of the hypotenuse (sin = opposite/hypotenuse).
- Cosine is the ratio of the length of the adjacent side to the length of the hypotenuse (cos = adjacent/hypotenuse).
- Tangent is the ratio of the length of the opposite side to the length of the adjacent side (tan = opposite/adjacent).
| 2. How do you find the values of trigonometric functions for common angles? | |
Ans. The values of trigonometric functions for common angles (0°, 30°, 45°, 60°, and 90°) can be found using the unit circle or special right triangles. For example:
- sin(0°) = 0, cos(0°) = 1, tan(0°) = 0
- sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) = 1/√3
- sin(45°) = √2/2, cos(45°) = √2/2, tan(45°) = 1
- sin(60°) = √3/2, cos(60°) = 1/2, tan(60°) = √3
- sin(90°) = 1, cos(90°) = 0, tan(90°) is undefined.
| 3. What is the Pythagorean theorem and how does it relate to trigonometry? | |
Ans. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). It can be expressed as a² + b² = c². This theorem is fundamental in trigonometry as it relates to the definitions of the sine, cosine, and tangent functions, which can be derived from the sides of a right triangle based on this relationship.
| 4. What is the difference between radians and degrees in trigonometry? | |
Ans. Radians and degrees are two units for measuring angles. Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle; one radian is the angle formed when the arc length is equal to the radius. To convert degrees to radians, you can use the formula: radians = degrees × (π/180). Conversely, to convert radians to degrees, use: degrees = radians × (180/π).
| 5. How can trigonometric functions be applied in real-life scenarios? | |
Ans. Trigonometric functions have various real-life applications, including:
- Engineering: calculating forces, angles, and distances in structures.
- Physics: analyzing waves, oscillations, and periodic motion.
- Navigation: determining positions and distances using angles.
- Architecture: designing buildings with specific angles and heights.
- Computer graphics: creating realistic animations and simulations using angles and distances.
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