Question

Please help!

flynn is playing with a toy that is tied to his hand by a string. the toy falls toward the floor then risee back towards flynns hand, and repeats this motion, following the path illustrated by the given graph. (see pic)

use the graph to complete the function h(t) that models the toys height, in feet, above the floor t seconds after it has left flynns hand.

h(t)=____ (poss. answers- 2, 1.75, 3.5, 4) cos=(____pi^t) poss. answers- 6, 1/6, 1/3, 3)
+_____ (poss. answers- 1.75, 0.25, 2, 2.25)

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Answer 1

h(t) = 1.75 cos (π/6) + 2.25

Explanation:

the amplitude of a regular cos graph is 1 (it alternates between +1 and -1 on the y-axis). that is, amplitude = (1 - -1)/2 = 2/2 = 1.

this graph has amplitude (4 - 0.5)/2 = 3.5/2 = 1.75.

the graph repeats for every sixth value on the x-axis (time axis).

in the x-axis direction, a cos graph that becomes 6 times larger is cos (π/6). a cos graph that becomes 6 times smaller is cos (6π).

so for our graph, it is cos (π/6).

what about the y-shift?

the graph has already been enlarged 1.75 times parallel to the y-axis.

it crosses the y-axis at 4. so the y-shift is 4 - 1.75 = 2.25.

so our graph is given by h(t) = 1.75 cos (π/6) + 2.25

Answer 2

Answer: got it right

h(t)=1.75, cos(1/3), + 2.25

Explanation: