Question

How have government and businesses impacted energy efficiency?

Answer 1

What are the graphs of y = sin x and y = sec x in the interval from -2pi to 2pi.

Answer 2

Government and businesses have both played a significant role in impacting energy efficiency in various ways. Here are a few examples:

Government:
1. Setting energy efficiency standards: Governments have set energy efficiency standards for appliances, automobiles, and equipment in the industrial and commercial sectors. For instance, the U.S. Department of Energy has set standards for appliances like refrigerators and air conditioners to help reduce energy consumption.
2. Offering incentives: Governments provide tax credits and subsidies for businesses that invest in energy-efficient technologies. For example, the U.S. federal government offers tax credits for individuals and businesses that invest in renewable energy sources like solar panels and wind turbines.
3. Regulations: Governments enact regulations to promote energy efficiency, such as building codes that require buildings to meet certain energy standards or laws that mandate energy efficiency upgrades in existing buildings.

Businesses:
1. Innovation in technology: Companies invest in developing new technologies that are energy efficient. For example, electric cars and LED lightbulbs are examples of energy-efficient products developed by businesses.
2. Sustainable practices: Many businesses have implemented sustainable practices like reducing paper use, optimizing supply chain logistics, and adopting efficient building systems.
3. Partnership with government: Some businesses partner with government to implement energy efficiency initiatives. For instance, large businesses may collaborate with government agencies to retrofit public buildings with energy-efficient technologies.

Answer 3

Here are the graphs of y = sin(x) and y = sec(x) in the interval from -2π to 2π:

Graph of y = sin(x):

```
1 ┌─○────○────○────○────○────○────○────○────○────○────○─┐
│ │
│ │
│ │
│ │
│ ┌──○──┐ │
0.5╎ │ │ │
│ │ │ │
│ │ │ │
│ │ │ │
│ └──○──┘ │
0├─────────────○───────────○─────────────○─────────────┤
│ │
-0.5╎ │ │
│ │
│ │
│ │
│ │
-1 └─○────○────○────○────○────○────○────○────○────○────○────○─┘
-2π -3π/2 -π -π/2 0 π/2 π 3π/2 2π
```

Graph of y = sec(x):

```
│ ┌○─────────────────────────────┐
│ │ │
│ │ │
│ │ │
│ │ │
│ │ │
│ └───────────────────────────────○─┘
5 │ │
│ │
│ │
│ │
│ │
│ │
0 ┼────○────○─────────────────○────○───────○─────────────┤
│ │
│ │
-5 │ │
│ │
│ │
│ │
│ │
└───────────────────────────────────────────────────────┘
-2π -3π/2 -π -π/2 0 π/2 π 3π/2 2π
```

Notes:
- The sine function (y = sin(x)) is a periodic function, oscillating between the values of -1 and 1. It has 2π as its period and crosses the x-axis at integer multiples of π.
- The secant function (y = sec(x)) is not periodic - it has vertical asymptotes where its value is undefined (at the points where cos(x) = 0, i.e. at odd multiples of π/2) and its value oscillates between positive and negative values elsewhere.