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In Problems 79-84, use the following discussion. The formula can be used to approximate the number of hours of daylight D when the declination of the Sun is at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, must be expressed in radians.
Approximate the number of hours of daylight at the Equator ( north latitude) for the following dates:
Summer solstice
Vernal equinox
July 4
What do you conclude about the number of hours of daylight throughout the year for a location at the Equator?
![Check Mark](/static/check-mark.png)
To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight at the equator ( north latitude), for the following dates:
a. Summer solstice .
Answer to Problem 73AYU
Solution:
a. hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
a. Summer solstice .
Formula used:
Calculation:
a. Summer solstice north latitude.
Convert degree into radians.
hours.
![Check Mark](/static/check-mark.png)
To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight at the equator ( north latitude), for the following dates:
b. Vernal equinox .
Answer to Problem 73AYU
Solution:
b. hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
b. Vernal equinox .
Formula used:
Calculation:
b. Vernal equinox ; north latitude.
Convert degree into radians.
hours.
![Check Mark](/static/check-mark.png)
To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight at the equator ( north latitude), for the following dates:
c. July 4 .
Answer to Problem 73AYU
Solution:
c. hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
c. July 4 .
Formula used:
Calculation:
c. July 4 north latitude.
Convert degree into radians.
hours.
![Check Mark](/static/check-mark.png)
To calculate: The number of hours of daylight at the location north latitude Approximate the number of hours of daylight at the equator ( north latitude), for the following dates:
d. The number of hours of daylight throughout the year for a location at the equator.
Answer to Problem 73AYU
Solution:
d. The number of hours of daylight throughout the year for a location at the equator hours.
Explanation of Solution
Given:
The declination of the Sun is defined as the angle between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth.
d. north latitude .
Formula used:
Calculation:
d. The number of hours of daylight throughout the year for a location at the equator hours.
Chapter 7 Solutions
Precalculus Enhanced with Graphing Utilities
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