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Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of sin -1(1) + sin-1(1/√2) is
- a)2π
- b)π
- c)3π/4
- d)π/3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Direction: Read the following text and answer the following questions...
Sin-1(1) + sin-1(1/√2) = π//2 + π/4
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= 3π/4
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Direction: Read the following text and answer the following questions...
Principal Value of Inverse Trigonometric Functions
Introduction:
Inverse trigonometric functions are the inverse functions of trigonometric functions. They are used to find the angle measures corresponding to given trigonometric ratios. The principal branch refers to the values of the inverse trigonometric functions that lie within a specific range.
Principal Value:
The principal value of an inverse trigonometric function is the value that lies within the range of the principal branch. In other words, it is the value of the inverse trigonometric function that is considered as the primary or principal value. For example, the principal value of sin^(-1)(1) is denoted as sin^(-1)(1) and represents the angle whose sine is 1.
Finding the Principal Value of sin^(-1)(1):
To find the principal value of sin^(-1)(1), we need to determine the angle whose sine is 1. The sine function takes values between -1 and 1, inclusive. Therefore, we need to find the angle in the principal branch whose sine is 1.
Determining the Angle:
We know that the sine function is positive in the first and second quadrants. In the first quadrant, the sine function is positive and equal to 1 at π/2 radians or 90 degrees. Therefore, sin^(-1)(1) = π/2.
Finding the Principal Value of sin^(-1)(1/√2):
To find the principal value of sin^(-1)(1/√2), we need to determine the angle whose sine is 1/√2. The sine function takes values between -1 and 1, inclusive. Therefore, we need to find the angle in the principal branch whose sine is 1/√2.
Determining the Angle:
We know that the sine function is positive in the first and second quadrants. In the first quadrant, the sine function is positive and equal to 1/√2 at π/4 radians or 45 degrees. Therefore, sin^(-1)(1/√2) = π/4.
Conclusion:
The principal value of sin^(-1)(1) is π/2 and the principal value of sin^(-1)(1/√2) is π/4. Therefore, the correct answer is option C) 3π/4.
Introduction:
Inverse trigonometric functions are the inverse functions of trigonometric functions. They are used to find the angle measures corresponding to given trigonometric ratios. The principal branch refers to the values of the inverse trigonometric functions that lie within a specific range.
Principal Value:
The principal value of an inverse trigonometric function is the value that lies within the range of the principal branch. In other words, it is the value of the inverse trigonometric function that is considered as the primary or principal value. For example, the principal value of sin^(-1)(1) is denoted as sin^(-1)(1) and represents the angle whose sine is 1.
Finding the Principal Value of sin^(-1)(1):
To find the principal value of sin^(-1)(1), we need to determine the angle whose sine is 1. The sine function takes values between -1 and 1, inclusive. Therefore, we need to find the angle in the principal branch whose sine is 1.
Determining the Angle:
We know that the sine function is positive in the first and second quadrants. In the first quadrant, the sine function is positive and equal to 1 at π/2 radians or 90 degrees. Therefore, sin^(-1)(1) = π/2.
Finding the Principal Value of sin^(-1)(1/√2):
To find the principal value of sin^(-1)(1/√2), we need to determine the angle whose sine is 1/√2. The sine function takes values between -1 and 1, inclusive. Therefore, we need to find the angle in the principal branch whose sine is 1/√2.
Determining the Angle:
We know that the sine function is positive in the first and second quadrants. In the first quadrant, the sine function is positive and equal to 1/√2 at π/4 radians or 45 degrees. Therefore, sin^(-1)(1/√2) = π/4.
Conclusion:
The principal value of sin^(-1)(1) is π/2 and the principal value of sin^(-1)(1/√2) is π/4. Therefore, the correct answer is option C) 3π/4.
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Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer?
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Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer?.
Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of sin -1(1) + sin-1(1/√2) isa)2πb)πc)3π/4d)π/3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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