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Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it?
Most Upvoted Answer
Let f be an odd function defined on the set of real number such that f...
Solution:
Given, f(x) is an odd function defined on the set of real numbers such that for x greater than or equal to 0, f(x) = 3sinx 4cosx.
Since f(x) is an odd function, we can say that f(-x) = -f(x) for all x in the domain of f.
Therefore, for x greater than or equal to 0, we have
f(-x) = -f(x)
=> f(-11pi/6) = -f(11pi/6)
=> f(-11pi/6) = -3sin(11pi/6) + 4cos(11pi/6)
Now, we know that sin(11pi/6) = -1/2 and cos(11pi/6) = -sqrt(3)/2.
Substituting these values in the above equation, we get
f(-11pi/6) = -3(-1/2) + 4(-sqrt(3)/2)
=> f(-11pi/6) = 3/2 - 2sqrt(3)
Therefore, the correct option is 3. 3/2 - 2sqrt(3).
Explanation:
We are given an odd function f(x) which is defined on the set of real numbers such that for x greater than or equal to 0, f(x) = 3sinx 4cosx.
We need to find the value of f(x) at x = -11pi/6.
Since f(x) is an odd function, we can use the property f(-x) = -f(x) to find the value of f(-11pi/6).
Substituting the values of sin(11pi/6) and cos(11pi/6) in the expression for f(-x), we get the value of f(-11pi/6) as 3/2 - 2sqrt(3).
Therefore, the correct option is 3. 3/2 - 2sqrt(3).
Given, f(x) is an odd function defined on the set of real numbers such that for x greater than or equal to 0, f(x) = 3sinx 4cosx.
Since f(x) is an odd function, we can say that f(-x) = -f(x) for all x in the domain of f.
Therefore, for x greater than or equal to 0, we have
f(-x) = -f(x)
=> f(-11pi/6) = -f(11pi/6)
=> f(-11pi/6) = -3sin(11pi/6) + 4cos(11pi/6)
Now, we know that sin(11pi/6) = -1/2 and cos(11pi/6) = -sqrt(3)/2.
Substituting these values in the above equation, we get
f(-11pi/6) = -3(-1/2) + 4(-sqrt(3)/2)
=> f(-11pi/6) = 3/2 - 2sqrt(3)
Therefore, the correct option is 3. 3/2 - 2sqrt(3).
Explanation:
We are given an odd function f(x) which is defined on the set of real numbers such that for x greater than or equal to 0, f(x) = 3sinx 4cosx.
We need to find the value of f(x) at x = -11pi/6.
Since f(x) is an odd function, we can use the property f(-x) = -f(x) to find the value of f(-11pi/6).
Substituting the values of sin(11pi/6) and cos(11pi/6) in the expression for f(-x), we get the value of f(-11pi/6) as 3/2 - 2sqrt(3).
Therefore, the correct option is 3. 3/2 - 2sqrt(3).
Community Answer
Let f be an odd function defined on the set of real number such that f...
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Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it?
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Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it?.
Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be an odd function defined on the set of real number such that for x greater than or equal to 0, f(x)=3sinx 4cosx then f(x) at x = -11pi÷6. (1. 3÷2 2root3 2. -3÷2 2root3 3.3÷2-2root2 4. -3÷2-2root3)which of these option is correct and explain it?.
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