What trigonometric function represents the graph?
What trigonometric function best represents the given graph?
a. f(x) = 4 sin(x - π/2)
b. f(x) = 4 cos(x - π/2)
c. f(x) = 4 sin(x - π/2) + 1
d. f(x) = 4 cos(x - π/2) + 1
Please provide any additional context or characteristics of the graph that may help in determining the correct function.
2 Answers
I would say: a. f(x) = 4 sin(x -pi/2).
We can throw out C and D because there’s no vertical shift.
VS = .5(Max+Min) so .5(4+-4) = .5(0) = 0.
If you know your standard sine and cosine graphs, then it becomes visible that A is the answer. A proper cosine function for the graph would be f(x) = 4 cos(x – pi). The phase shift was off for choice B.
a. f(x) = 4 sin(x -pi/2)
There is not a vertical shift, so the answer automatically cannot be c. or d. A vertical shift is found by adding the maximum and minimum y-values and then dividing the answer by 2. So you have (-4+4)/2= 0/2= 0. With 0, there is not a vertical shift.
There is a phase shift of pi/2, which means the normal function’s graph is moved over pi/2 units to the right. This phase shift is found in the parentheses of (x- pi/2)–because the pi/2 is being subtracted, the graph is moved this many units to the right. A standard sine function has the point (0,0), and this means the point becomes (0, pi/2), which is shown. A standard cosine function has the point (pi/2, 0), and this would mean the point (pi/2, 0) becomes (pi, 0), and this is not shown.
Therefore, the answer is a.
Related Questions
Find the circumference of a circle with a radius of 5 inches. Please express your answer in terms of pi.
How tall is 77 inches when converted to feet?
In circle O, ST is a diameter. What is the value of x if (2x + 8) equals one of the following options: 22.0, 25.0, 25.4,...
I have a question regarding torque in a magnetism context. I understand that the equation τ = IABsin(θ) will be relevant...
Could you please help me find the cube roots of the complex number represented in polar form as 8(cos 216° + i sin 216°)...
Please find below the present and future values for different interest rates. Compounding and discounting occur annually...
A radio telescope features a parabolic surface, as illustrated below. Given that the telescope is 1 meter deep and 12 me...
What is the cube root of ( b^{27} )?
How many moles of CuO can be produced from 0.450 moles of Cu2O in the following reaction: 2Cu2O + O2 → 4CuO?
Suppose you are asked to calculate the area of a rectangle that is 2.1 cm wide and 5.6 cm long. Your calculator provides...