diagram not to scal Topic 3 Trig Function graphs [52 marks] 1. A Ferris wheel with diameter 110 metres rotates at a constant speed. The lowest point on the wheel is 10 metres above the ground, as shown on the following diagram. P is a point on the wheel. The wheel starts moving with P at the lowest point and completes one t revolution in 20 minutes. 110m The height, h metres, of P above the ground after t minutes is given by h(t) = a cos(bt) + c, where a, b, c E R. d 10m Find the values of a, b and c. [5 marks] fohom S bnaobbwoldswdad s giod isons

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
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Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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RIX
Topic 3 Trig Function graphs [52 marks]
diagram not to scalk
1. A Ferris wheel with diameter 110 metres rotates at a constant speed.
The lowest point on the wheel is 10 metres above the ground, as
shown on the following diagram. P is a point on the wheel. The
wheel starts moving with P at the lowest point and completes one
revolution in 20 minutes.
110m
The height, h metres, of P above the ground after t minutes is
given by h(t) = a cos(bt) + c, where a, b, c E R. Sd ee
Find the values of a, b and c. [5 marks]
10m
ahom S
bnsobb wol nes
2. Considèr the graph of the function f (x) = 2 sin x,
0sx < 2n. The graph of f intersects the line y = -1
exactly twice, at point A and point B. This is shown in the
following diagram.
1o sulev bnib
Consider the graph of g(x)
p > 0.
= 2 sin px, 0 s x < 2n, where
y=-1
Find the greatest value of p such that the graph of g does
not intersect the line y = -1. [3 marks]
A
Transcribed Image Text:RIX Topic 3 Trig Function graphs [52 marks] diagram not to scalk 1. A Ferris wheel with diameter 110 metres rotates at a constant speed. The lowest point on the wheel is 10 metres above the ground, as shown on the following diagram. P is a point on the wheel. The wheel starts moving with P at the lowest point and completes one revolution in 20 minutes. 110m The height, h metres, of P above the ground after t minutes is given by h(t) = a cos(bt) + c, where a, b, c E R. Sd ee Find the values of a, b and c. [5 marks] 10m ahom S bnsobb wol nes 2. Considèr the graph of the function f (x) = 2 sin x, 0sx < 2n. The graph of f intersects the line y = -1 exactly twice, at point A and point B. This is shown in the following diagram. 1o sulev bnib Consider the graph of g(x) p > 0. = 2 sin px, 0 s x < 2n, where y=-1 Find the greatest value of p such that the graph of g does not intersect the line y = -1. [3 marks] A
Expert Solution
Step 1

As per our guidelines, we are supposed to answer only one question at a time.

 

Given data are:

Diameter=110 m,

So radius= 55 m.

Angular speed ω = 1 revolution in 20 minutes. = 2π20 minute-1

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