What does the midline, period, amplitude, and horizontal shift of a graph represent in the real world? For example, if I'm evaluating a sin function graph, and the points on the scatter plot represent temperatures for a certain city from one year to the next, what do the terms really represent?

Q: What is the domain of the cosine function?

A: We know that domain of cosine function is all real numbers as cosine function is defined for any…

Q: Is the sine function even, odd, or neither? Is its graph symmetric? With respect to what?

A: To find:  If the sine function even or odd Is the graph symmetric and with respect to what.

Q: . What happens to the graph of a trigonometric function if it has a positive phase shift?

A:

Q: What is the equation of a sine or cosine function to describe the graph?

A: Let the function corresponding to the given graph be f(x).  From the graph, we can observe that if…

Q: Why are trigonometric functions ideally suited to model phenomena that repeat in cycles?

A: Trigonometric functions sin, cos, tan, cosec, sec, and cot are periodic functions. That is after…

Q: Find the amplitude and the equation of the midline of the period function graphed below. 10 -5 10

A: This is a problem of harmonic motion.

Q: What is the range of the sine function?

A: We know, domain of sine function is all real numbers. Also, -1≤sinx≤1 ⇒range of sinx is [-1,1].

Q: Can the sin x ever be a value greater than 1?

A: We have to find the sinx value

Q: Why sometimes the graph of a trigonometric function oscillates very rapidly?

A:

Q: Find the exact value of:

A: To find the value of: tan-1(-3) Solution: We know that domain of function tan-1(x) is,-π2<x<π2…

Q: What are the amplitude and period of the function graphed below?

A: Amplitude : It is half the difference between the maximum and minimum of a periodic function. Period…

Q: Evaluate the given expression without the aid of a calculator x + 1 tan[arcsin(-

A:

Q: Is the sine function even, odd, or neither?

A: We know that, a function fx is said to be even if and only if f-x=fx. Also a function fx is said to…

Q: Explain how to sketch the graphs of y = sin(x) and y = cos(x) and explain how to find the period,…

A: Explanation and solutions is given below....

Q: 4. State the domain and the range of the cosine function.

A: The domain and range of Cosine function is determined directly from its definition. Cosine function…

Q: How do you convert the given cosine to the given sine function in the attached image?

A: To convert cosine in y=6 cos π7t  to y=6sinπ7t+72.

Q: the graphs of y= sinx and y=cosx differ by a horizontal shift of _____?

A: The graph of y=sinx and y=cosx is shown below:

Q: This is a graph of someone on a swing, measuring height of swing vs time. What is the amplitude and…

A: From the graph  Amplitude  = 2 - 0.92=0.55 m

Q: Use a graphing calculator to evaluate tan (4) 7 Round your answer to three decimal places. tan…

A: Giventan(4π7)

Q: Does this graph have the shape of sin(x) or cos(z)? | What is the period of the graphed function?…

A: (a) This graph has the shape of sin (x).

Q: Draw graphs to show the difference in sine and cosine functions.

A: Consider the functions y=sin x  and   y=cos x. Sketch the graph of both functions as shown below.

Q: Illustrate the Graphs of the sine and cosine functions?

A: Given- Sine function and cosine function. To draw- The graph of sine function and cosine function.…

Q: 5. Sketch a well-labeled graph of the function along with its corresponding sine or cosine function.…

A: Giveny=-10cscx4+10.

Q: What is a periodic function? Why are the sine and cosine functions periodic?

A: Periodic function is a function which repeats its value after a regular interval. If fx+T=fx then…

Q: One period of a sine or cosine function is one ________ of the sine or cosine curve.

A: To fill in the blank in the given statement, " One period of a sine or cosine function is one…

Q: How does the formula for the general sine function ƒ(x) = A sin ((2pai/B)(x - C)) + D relate to the…

A: Consider the given sine function.

Q: What is the period of the cosine function?

A: Given,          The period of the cosine function .

Q: What is the range of the cosine function?

A:

Q: Why would a sine function be used to model the number of daylight hours?

A: We have to explain why a sine function is used to model the number of daylight hours.

Q: State the definition of the hyperbolic cosine and hyperbolic sine functions.

A: We define hyperbolic cosine and sine function as,

Q: Write an equation for a function with the given characteristics. A sine curve with a period of 81,…

A:

Q: State the definitions of the hyperbolic cosine and hyperbolic sine functions.

A: Given sine and cosine function.

Q: sine curve with a period of 4T, an amplitude of 5, a left phase shift and a vertical translation own…

A:

Q: Write the equation of a sine or cosine function to describe the graph. 5- 3. 15 -- 4 2 talt 4.

A: In the given problem we have to define sine or cosine function.

Q: Find the amplitude, equation of the midline, period of the function, and equation of the function…

A:

Q: Determine the amplitude, midline, period, and an equation involving the sine function for the graph…

A: Determine the amplitude, midline, period, and an equation involving the sine function for the graph.…

Q: Find the exact value of the expression. tan arcsin 2

A:

Q: Write the equation of a sine or cosine function to describe the graph. 2n 6. -1 2. 3 6. -4 -5- -6 3.

A: Given: The graph of sine or cosine function as To find: The equation of function.

Q: Show that cosine is an even function and sine is odd.

A: We have to prove that f(x)=cos(x)  is an even function and g(x)=sin(x) is even function .

Q: If y = tan-1(-1), find the value of y without use Calculator.

A: To find: The value of y without using calculator: Given: The equation is y=tan-1-1. Concept used:…

Q: If the sine function whose graph is the graph of y = -2 sin 2 (x – -) + 1 shifted 4. units to the…

A: To find the equation after the transformations given

Q: Find the equation of the cos function whose graph is the graph of y = - 2 cos 2(x-pi/4)+1 shifted…

A: We have to find the equation of the cos function whose graph is the graph of y=-2cos2x-π4+1 shifted…

Q: Question 5 What is the period of the tangent function?|

A: We have to find period of tangent function

Q: How do you find the period for a sine function by looking at its graph?

A: Given,  The graph of sine function.

Q: The graph of y=tan(4x) is shown below. What is the period of the function?

A: We have to find the period of tangent function.

Q: Examine the graph below and determine the amplitude, period, phase shift, and vertical shift of each…

A: Given graph is of sine which is a periodic function. Amplitude is defined as the height from the…

Q: When does the graph of a trigonometric function oscillate very rapidly?

A: We know that as x approaches to zero, the function sin(1/x) oscillates infinitely or very rapidly.

Q: 2. y = 4 sin (-2 [I x + II) + 3

A: To find  amplitude, period, phase shift, vertical shift, range

Q: The graph shows the variation of the water level relative to mean sea level in Commencement Bay at…

A: Given form of equation  y= a sinbt

Q: What is the amplitude of the sine function? What does this tell you about the graph?

A: If the function is given as y=sinx is called the sine function. For the value of x as, -π2≤x≤π2…