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Consider the following statements:
1. The function f(x) = sin x decreases on the interval (0, π/2).
2. The function f(x) = cos x increases on the interval (0, π/2).
1. The function f(x) = sin x decreases on the interval (0, π/2).
2. The function f(x) = cos x increases on the interval (0, π/2).
Which of the above statements is/are correct ?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'D'. Can you explain this answer?
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Consider the following statements:1. The function f(x) = sin x decreas...
sin x increases on the interval 
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Consider the following statements:1. The function f(x) = sin x decreas...
1. The function f(x) = sin x decreases on the interval (0, π/2).
This statement is false. The function f(x) = sin x increases on the interval (0, π/2). The function starts at 0 when x = 0, and as x increases, sin x also increases, reaching its maximum value of 1 at x = π/2.
2. The function f(x) = sin x is periodic with a period of 2π.
This statement is true. The function f(x) = sin x repeats itself every 2π units. This means that if you shift the graph of sin x by any multiple of 2π, it will look exactly the same.
3. The function f(x) = sin x is an odd function.
This statement is true. An odd function is a function that satisfies the property f(-x) = -f(x) for all x in its domain. For the function f(x) = sin x, we have sin(-x) = -sin(x), which shows that it is an odd function.
4. The function f(x) = sin x is defined for all real numbers.
This statement is true. The function f(x) = sin x is defined for all real numbers. The input x can be any real number, and the output will be a value between -1 and 1.
This statement is false. The function f(x) = sin x increases on the interval (0, π/2). The function starts at 0 when x = 0, and as x increases, sin x also increases, reaching its maximum value of 1 at x = π/2.
2. The function f(x) = sin x is periodic with a period of 2π.
This statement is true. The function f(x) = sin x repeats itself every 2π units. This means that if you shift the graph of sin x by any multiple of 2π, it will look exactly the same.
3. The function f(x) = sin x is an odd function.
This statement is true. An odd function is a function that satisfies the property f(-x) = -f(x) for all x in its domain. For the function f(x) = sin x, we have sin(-x) = -sin(x), which shows that it is an odd function.
4. The function f(x) = sin x is defined for all real numbers.
This statement is true. The function f(x) = sin x is defined for all real numbers. The input x can be any real number, and the output will be a value between -1 and 1.
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Consider the following statements:1. The function f(x) = sin x decreases on the interval (0, π/2).2. The function f(x) = cos x increases on the interval (0, π/2).Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?
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