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Questions
1. If sin 3θ = cos (θ – 6)° and 30 and (θ – 6)° are acute angles, find the value of θ.
2. If 3 cot A = 4, find the value of 
.
3. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
Determine:
(i) sin A, cos A
(ii) sin C, cos C
4. Evaluate 2tan2 45° + cos2 30° – sin2 60°.
5. If sin θ + cos θ = √2, then evaluate tan θ + cot θ.
6. If sin θ + sin2θ + sin3θ = 1, then find the value of cos6 θ – 4 cos4 θ + 8 cos2 θ.
7. What is the value of 0, for sin2θ = 1, where 0° < θ < 90°?
8. In ∆ABC, ∠B = 90°. If AB = 14 cm and AC = 50 cm then tan A equals?
9. If 4 cot θ = 3 then what is the value of 
?
10. What is the value of cosec2 27° – tan2 63°?
11. If ∆ABC is right angled at C, then what is the value of cos(A + B)?
12. If 3 cos θ = 1, then what is the value of 
?
13. Evaluate 
14. If sin 3θ = cos (θ – 6)° and 30 and (θ – 6)° are acute angles, find the value of θ.
15. If sec 3A = cosec (A – 10°) where 3A is an acute angle, find the value of A.
Answers
1. θ = 24°
2. 17/8
3. (i) Sin A = 7/25 and cos A = 24/25
(ii) Sin C = 24/25 and Cos C = 7/25
4. 2
5. 2
6. 4
7. 45°
8. 7/24
9. 1/7
10. 1
11. 0
12. 10
13. 2
14. θ = 24°
15. A = 25°
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FAQs on Practice Questions: Introduction to Trigonometry - Mathematics (Maths) Class 10
| 1. What is the Pythagorean theorem and how is it applied in trigonometry? |  |
| 2. How do you find the sine, cosine, and tangent of an angle in a right triangle? | |
Ans. To find the sine, cosine, and tangent of an angle (let's say angle A) in a right triangle, you use the following definitions:
- Sine (sin A) is the ratio of the length of the opposite side to the hypotenuse (sin A = opposite/hypotenuse).
- Cosine (cos A) is the ratio of the length of the adjacent side to the hypotenuse (cos A = adjacent/hypotenuse).
- Tangent (tan A) is the ratio of the length of the opposite side to the adjacent side (tan A = opposite/adjacent).
| 3. What are the key trigonometric identities that students should memorize? | |
Ans. Key trigonometric identities include:
- Pythagorean identities: sin²x + cos²x = 1.
- Angle sum identities: sin(A + B) = sin A cos B + cos A sin B; cos(A + B) = cos A cos B - sin A sin B.
- Double angle formulas: sin(2x) = 2sin x cos x; cos(2x) = cos²x - sin²x.
| 4. What is the unit circle and why is it important in trigonometry? | |
Ans. The unit circle is a circle with a radius of one centered at the origin of the coordinate plane. It is important in trigonometry because it provides a way to define the sine, cosine, and tangent functions for all angles, not just those in right triangles. Points on the unit circle correspond to the values of these functions, allowing for a visual representation of their behavior and periodicity.
| 5. How can trigonometry be applied in real-life scenarios? | |
Ans. Trigonometry has numerous real-life applications, including:
- In architecture and engineering, to calculate structural loads and angles.
- In navigation, for determining distances and angles between locations.
- In physics, to analyze wave patterns and oscillations.
- In computer graphics, for rendering 3D images and animations.
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