Answer:
Functions Range
y = 3sin(x - π ) : [-3, 3]
y = 1 - sin(x) : [0, 2]
y = 3 + 4cos(x - π) : [-1, 7]
y = 2 + cot(x) : (-∞, ∞)
Step-by-step explanation:
The Range is the output values of the function.
The range of sin(x) and cos(x) function is [-1, 1]
The range of tan(x) and cot(x) function is (-∞, ∞).
The range of cosec(x) and sec(x) function is (-∞ , -1] U [1 , + ∞).
1. y = 3sin(x - π ) Here range of y is 3 times of [-1, 1]
Hence, Range of y = [-3, 3]
2. y = 1 - sin(x) = 1 - [-1, 1] = [0, 2]
Hence, Range of y = [0, 2]
3. y = 3 + 4cos(x - π) Here range of y is 4 times of [-1, 1] + 3
⇒ 4 × -1 + 3 = -1 and 4 × 1 + 3 = 7
Hence, Range of y is [-1, 7].
4. y = 2 + cot(x) Since, range of cot(x) = (-∞, ∞)
so, adding any number in (-∞, ∞) is also (-∞, ∞).
Hence, Range of y is (-∞, ∞).
