(a) Express 2 sin e - 1.5 cos e in the form R sin (0 – a), where R>0 and 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section: Chapter Questions
Problem 19T
Question
(a)
Express 2 sin e - 1.5 cos e in the form R sin (0 – a), where R>0 and
0<a<.
Give the value of a to 4 decimal places.
(b) (i) Find the maximum value of 2 sin 0 – 1.5 cos 0.
(ii) Find the value of 0, for 0 <0< n, at which this maximum occurs.
Tom models the height of sea water, H metres, on a particular day by the equation
4nt
4nt
H= 6+2 sin
- 1.5 cos
25
0st<12,
25
where t hours is the number of hours after midday.
(c) Calculate the maximum value of H predicted by this model and the value of t, to 2
decimal places, when this maximum occurs.
(d) Calculate, to the nearest minute, the times when the height of sea water is predicted, by
this model, to be 7 metres.
Transcribed Image Text:(a) Express 2 sin e - 1.5 cos e in the form R sin (0 – a), where R>0 and 0<a<. Give the value of a to 4 decimal places. (b) (i) Find the maximum value of 2 sin 0 – 1.5 cos 0. (ii) Find the value of 0, for 0 <0< n, at which this maximum occurs. Tom models the height of sea water, H metres, on a particular day by the equation 4nt 4nt H= 6+2 sin - 1.5 cos 25 0st<12, 25 where t hours is the number of hours after midday. (c) Calculate the maximum value of H predicted by this model and the value of t, to 2 decimal places, when this maximum occurs. (d) Calculate, to the nearest minute, the times when the height of sea water is predicted, by this model, to be 7 metres.
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