Determine the minimum and maximum value of the following trigonometric function.f, of, x, equals, minus, 3, sine, x, plus, 1f(x)=−3sinx+1
Question
Determine the minimum and maximum value of the following trigonometric function.
The function is given by:
Solution
The function given is f(x) = -3sin(x) + 1.
Step 1: Identify the amplitude of the function The amplitude of the function is the absolute value of the coefficient of the sine function, which is |-3| = 3.
Step 2: Identify the vertical shift of the function The vertical shift of the function is the constant term, which is +1.
Step 3: Determine the minimum and maximum values The minimum and maximum values of a sine function occur at the peak and trough of its wave, respectively. Since the amplitude of the function is 3, the wave of the function goes 3 units up and 3 units down from its vertical shift.
Therefore, the minimum value of the function is 1 - 3 = -2 and the maximum value of the function is 1 + 3 = 4.
Similar Questions
Determine the minimum and maximum value of the following trigonometric function.f, of, x, equals, minus, 3, sine, x, plus, 1f(x)=−3sinx+1
Let 𝑓(𝑥)=𝑥3−3𝑥2+2𝑥f(x)=x 3 −3x 2 +2x. Find the maximum and minimum values of the function 𝑓(𝑥)f(x) on the interval [0,3][0,3].
If f(x)=cos|x|−2ax+b𝑓(𝑥)=cos|𝑥|-2𝑎𝑥+𝑏 and function f𝑓 increases for all x𝑥 then find the maximum value of 2a+1
Find the equilibrium point, the maximum and the minimum values for the the following trigonometric function. Sketch the graph in your notebook.𝑓(𝑥)=4cos(4𝑥)+4
Suppose that 4 ≤ f ′(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(6) − f(3)? ≤ f(6) − f(3)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.