# Really simple trig modeling question

• lektor
In summary, the average hours of sunlight can be modeled by the equation 1.5*cos((pi*(x-3))/26)+6.5, where x represents the number of weeks since the start of the year. The greatest average number of sunlight per day is expected when PI*(x-3)/26 equals 0 or 360, and the least is expected when it equals 180 or (180+360). This is because cos 0 equals 1, giving the maximum, and cos 180 equals -1, giving the minimum. By solving for x, the week of the year with the least amount of expected sunlight can be determined.
lektor
The average hours of sunlight can be modeled on

$$1.5\cos \frac {\pi(x-3)}{26}+6.5$$ where x is the number of weeks since the start of the year.

Ok. so it isn't really the calculation questions which are getting me, unfortunately it is just the reading of the model..

Here are the 2 questions i wasn't sure about

b) What is the greatest average number of sunlight per day expected in nelson and when.

c) in which week of the year would you expect the least.

Thanks in advance to thoose who help :)

How do you those nice writing anyway?

For B)
its when PI*(x - 3)/26 = 0 or 360 etc...
for C)
its when PI*(x-3)/26 = 180 or (180 + 360) etc ...

why?
cos 0 = 1 thus giving maximum
cos 180 = -1 thus giving minimum

Just solve for x
hope this helps!

yeah man cheers, i figured it out just after i posted, i ignored the horizontal displacement :)

and as for the fancey writing :P

click my writing and then there should be something about a tutorial for it :0

## 1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

## 2. How is trigonometry used in modeling?

Trigonometry is used in modeling to solve real-world problems involving angles and distances, such as calculating the height of a building or the distance between two objects.

## 3. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions relate the ratios of the sides of a right triangle to its angles.

## 4. Can you provide an example of a trigonometric modeling problem?

Sure, a common example is calculating the height of a flagpole using the angle of elevation and the distance from the base of the flagpole to the observer.

## 5. What are some practical applications of trigonometry in the real world?

Trigonometry is used in various fields such as engineering, physics, and navigation. It is also used in architecture, surveying, and astronomy.

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