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Evaluate sin(3 sin–10.4)
a)0.56
b)0.31
c)0.64
d)0.9
Correct answer is 'D'. Can you explain this answer?
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Verified Answer
Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'....
3sin^-1(x) = sin^-1(3x - 4x^3) when -1/2<=x<=1/2
Definitely 0.4 comes in this range of x and so
Definitely 0.4 comes in this range of x and so
3sin^-1(0.4) = sin^-1[3*0.4 - 4*0.4^3]
3sin^-1(0.4) = sin^-1[1.2 - 4*0.064]
3sin^-1(0.4) = sin^-1[1.2 - 0.256]
3sin^-1(0.4) = sin^-1[0.944]
3sin^-1(0.4) = sin^-1[1.2 - 4*0.064]
3sin^-1(0.4) = sin^-1[1.2 - 0.256]
3sin^-1(0.4) = sin^-1[0.944]
Finally , sin(3sin^-1(0.4)) = sin{sin^-1(0.944)} = 0.944
Most Upvoted Answer
Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'....
Solution:
We know that sin–1x lies between –π/2 and π/2, so sin(3 sin–1 0.4) is valid.
Let sin–1 0.4 = θ, then sinθ = 0.4
Now, sin(3θ) = 3sinθ - 4sin^3θ
= 3 x 0.4 - 4 x 0.4^3
= 1.2 - 0.064
= 1.136
Therefore, sin(3 sin–1 0.4) = sin(1.136)
= 0.9
Hence, the correct answer is (d) 0.9.
We know that sin–1x lies between –π/2 and π/2, so sin(3 sin–1 0.4) is valid.
Let sin–1 0.4 = θ, then sinθ = 0.4
Now, sin(3θ) = 3sinθ - 4sin^3θ
= 3 x 0.4 - 4 x 0.4^3
= 1.2 - 0.064
= 1.136
Therefore, sin(3 sin–1 0.4) = sin(1.136)
= 0.9
Hence, the correct answer is (d) 0.9.
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Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'....
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Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. Can you explain this answer?
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Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. 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 Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. Can you explain this answer?.
Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. 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 Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate sin(3 sin–10.4)a)0.56b)0.31c)0.64d)0.9Correct answer is 'D'. Can you explain this answer?.
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