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Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

True and False

Q1: cosA = 4/3 for some angle A.
Ans: False

Q2: tanA = sinA/cosA
Ans: True

Q3: secA = 1cosA, for an acute angle
Ans: True

Q4: sin60º = 2sin30º
Ans: False

Q5: SinA + CosA = 1
Ans: False

Short Answer Questions

Q6: Write the values cos 0°, cos 45°, cos 60° and cos 90°. What happens to the values of cos as angle increases from 0° to 90°?
Ans: cos0 = 1
cos45 = 1/√2
cos 60 = 1/2
cos 90∘ = 0
We can see that values of cos decreases as angle increases from 0° to 90°

Q7: Write the values of tan 0°,tan 30°, tan 45°, tan 60° and tan 90°. What happens to the values of tan as angle increases from 0° to 90°?
Ans:
 tan 0 = 0
tan 30 = 1/√3
tan 60 = √3
cos 90∘ = undefined
We can see that values of cos decreases as angle increases from 0° to 90° 

 
Q8: If cosec A = √10 . find other five trigonometric ratios.
Ans:
Given cosec A = √10
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Now By Pythagoras theorem
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

Q9: The value of (sin 30 + cos 30) − (sin 60 + cos 60) is
Ans:
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

Q10: Evaluate the following: 2sin2 30 − 3cos245 + tan260
Ans:
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

Q11: Evaluate:
cot230∘  − 2cos260 − 3/4sec245 − 4sec230
Ans:
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

Q12: Write the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90°. What happens to the values of sin as angle increases from 0° to 90°?
Ans:
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
We can see that values of sin increases as angle increases from 0° to 90°

Q13: If sin A = 3/5 .find cos A and tan A.
Ans:

Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Now By Pythagoras theorem
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

Q14: In a right triangle ABC right angled at B if sinA = 3/5. find all the six trigonometric ratios of C.
Ans:

Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Now By Pythagoras theorem
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8
Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

Q15: If sinB = 1/2 , show that 3 cosB − 4 cos3B = 0
Ans:

Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

The document Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Introduction to Trigonometry Class 10 Worksheet Maths Chapter 8

1. What is the basic definition of trigonometry?
Ans.Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles, particularly right triangles. It focuses on the functions sine, cosine, and tangent, which relate the angles of a triangle to the ratios of its sides.
2. What are the primary trigonometric functions and how are they defined?
Ans.The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan). They are defined as follows for a right triangle: - Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. - Cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. - Tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
3. How do you calculate the sine, cosine, and tangent of common angles like 0°, 30°, 45°, 60°, and 90°?
Ans.The sine, cosine, and tangent values for common angles are: - 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.
4. What is the Pythagorean theorem and how is it related to trigonometry?
Ans.The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), expressed as a² + b² = c². This theorem is fundamental in trigonometry as it provides a way to relate the sides of a triangle, and it is used to derive the relationships between the trigonometric functions.
5. How can trigonometry be applied in real life?
Ans.Trigonometry has many practical applications in real life. It is used in fields such as engineering, physics, astronomy, architecture, and even in navigation and computer graphics. For example, architects use trigonometry to calculate structural loads, while surveyors use it to measure distances and angles in land surveying.
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