Question

Help confused with applying cosine and sine functions

Answer 1

A clock with an hour hand that is 12 inches long is hanging on a wall. At noon, the vertical distance between the tip of the hour hand and the ceiling is 21 inches. At 3 P.M., the distance is 33 inches; at 6 P.M., 45 inches; at 9 P.M., 33 inches; and at midnight the distance is again 21 inches. If f(x) represents the distance between the tip of the hour hand and the ceiling x hours after noon, write the function that represents this situation in the form of f(x) = acos(bx) + d.

Answer 2

would this be -33cos(pi/6)+12?

Answer 3

@mathmath333

Answer 4

x(time) y(distance from ceiling) Points
Noon 21 in (0,21)
3 PM 33 in (3,33)
6 PM 45 in (6,45)
9 PM 33 in (9,33)
Midnight 21 in (12,21)




https://www.desmos.com/calculator/mlivkkzyts

Answer 5

That a really handy website

Answer 6

whats the formula for amplitude

Answer 7

f(θ) = asinθ

Answer 8

here the highest value of y=45 and smallest is 21
so\((45-21)/2=12\\
a=12\)

Answer 9

so that means you amplify if by 12?

Answer 10

yes

Answer 11

now we have to find b

Answer 12

Based on the points isn't that pi?

Answer 13

the clock repeats 12 hrs so
\(b=2\pi/12=\pi/6\)

Answer 14

now d

Answer 15

vertical shift

Answer 16

well so we know 9 and 3 are both 33 inches and it makes the x axis