a.
To explain: Why the value of
For any sign change of
Given information:
Sinusoidal equation is given by,
Calculation:
Considering the equation,
It is noted that the sine function is odd from the given equation.
Therefore, for any sign change of
b.
To prove: The equation
Given information:
The given equations are,
Proof:
Since a sine curve is identical to a cosine curve offset to the right by
Rewriting the above cosine curve in terms of a sine function,
c.
To graph: The unit circle argument for the identity
Given information:
The identity is given by
Graph:
From the given identity,
Interpretation:
The graph indicates the arbitrary angle
d.
To prove: The equation
Given information:
The given equations are,
Proof:
Consider the two given identities and relating both to get,
Substitute
If
Therefore, both the identity has the same graph for the chosen value
e.
To prove: Any sinusoid can be represented
Given information:
The given equations are,
Proof:
Comparing all the results from part (a) to (d), it is known that,
The equation includes all requirements for vertical shifting
Therefore, for any sinusoid it can be represented by the equation
Chapter 4 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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- Evaluate the integral using any appropriate algebraic method or trigonometric identity. S- dy 18 √2 (1+y2/3) yarrow_forward4. Suppose the demand for a certain item is given by D(p)=-2 p² - 4p+350, where p represents the price of the item in dollars. a) Find the rate of change of demand with respect to price. b) Find and interpret the rate of change of demand when the price is $11.arrow_forward√3-x, x≤3, 2. For f(x) = 1 find each of the following. x > 3, x-3' 1. f(-6) 2. f(3) 3. f(7) 3. Find the domain of each of the following functions.arrow_forward
- 1. Using the definition of the derivative, find f'(x). Then find f'(2), f'(0) and f'(3) when the derivative exists. a) f(x)=5x²-6x-1arrow_forward2. f(x)=√7-x 4. A manufacturer has a monthly fixed cost of $40,000 and a production cost of $8 for each unit produced. The product sells for $12 per unit. 1. What is the cost function? 2. What is the revenue function? 3. Compute the profit corresponding to 12,000 units. 5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting x denote the length of one side of the base,arrow_forwardSolve using superposition principlearrow_forward
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