Trig Modelling Question

Original post by beachpanda

I'm stumped with this question and the working isn't shown - is anyone able to help?

"Adam wants to form a function to model the hours of daylight in his town throughout the year. He knows that the function should be of the form f(t) = A + Bcos(t), where A and B are positive constants and the time, t, is in radians."

a) The daylight hours vary from 7 to 17. Find the values of A and B.

What are the min and max values of cos? How can the be mapped (linearly) to a range [7,17]

Reply 2

OP

Original post by mqb2766

What are the min and max values of cos? How can the be mapped (linearly) to a range [7,17]

-1 ≤ cos(x) ≤ 1

But not sure how to map them to [7,17]?

Reply 3

Original post by beachpanda

-1 ≤ cos(x) ≤ 1

But not sure how to map them to [7,17]?

You could just pick some values for A and B and try? It's a simple "linear" transformation

Hint is that they're related to the midpoint and range of [7,17]

Reply 4

OP

Original post by mqb2766

You could just pick some values for A and B and try? It's a simple "linear" transformation

Hint is that they're related to the midpoint and range of [7,17]

Not really sure where to start with that to be honest?

Reply 5

Original post by beachpanda

Not really sure where to start with that to be honest?

If A = 2 and B = 3. What does -1 and 1 (range of cos) get mapped to?
It's probably easier than you think.

Reply 6

OP

Original post by mqb2766

If A = 2 and B = 3. What does -1 and 1 (range of cos) get mapped to?
It's probably easier than you think.

As it's Bcos(t) with B = 3, would it be -3 ≤ cos(t) ≤ 3 ?

Reply 7

Original post by beachpanda

As it's Bcos(t) with B = 3, would it be -3 ≤ cos(t) ≤ 3 ?

-3 <= Bcos() <= 3
Yes. So if you add A what happens?

B is obviously related t o the desired range and A to the shift of 0 to the midpoint?

Reply 8

OP

Original post by mqb2766

-3 <= Bcos() <= 3
Yes. So if you add A what happens?

B is obviously related t o the desired range and A to the shift of 0 to the midpoint?

Would it be:

- 1 ≤ 2 + 3cos(t) ≤ 5

Reply 9

Original post by beachpanda

Would it be:

- 1 ≤ 2 + 3cos(t) ≤ 5

That's correct. Hope you got [7,17] sorted.

Reply 10

OP

Original post by mqb2766

That's correct. Hope you got [7,17] sorted.

Just tried it and got there! @mqb2766 to the rescue again. Thankyou so much! :smile:

Reply 11