Trigonometry Answers

Prove that
(1-tan^2(theta÷2))(1-tan^2(theta÷2square))(1-tan^2(theta÷2cube)).... Infinity= theta dot cot(theta)

A submarine is on the surface of the ocean. The submarine then dives below the surface and travel a distance of 450 m while dropping a vertical distance of 300 m. determine the angle of depression and how far the submarine traveled horizontally

1. An autobike begins to on a level road directly toward a building that is 150 feet tall. How far does the
car travel during the time that the angle of elevation from the autobike to the top of the building changes from 27° to 36°

At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height of the rider is given for various times:
Time(s) 0 1 2 3 4 5 6 7 8 9
Height(m) 55 53 46 36 25 14 7 5 8 15

Find the amplitude, period, vertical translation, and phase shift for this function. [Note: that the table does not follow the bob through one complete cycle, so some thought will be required to answer this question.]

Determine the equation of the function in the form:
h(t) = asin [b(t – c)] + d.

How could the amplitude be determined without creating the graph or finding the function?

What would the rest position of the pendulum be?

What is the maximum displacement for this pendulum?

The time for one complete cycle is the period. How long would it take to complete 15 cycles?

The third-tallest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67sin [12(t + 0.0223)] + 70.
a. What is the diameter of this Ferris wheel?

b. Where is the rider at t = 0? Explain the significance of this value.

c.How high off the ground is the rider at the top of the wheel?

d. At what time(s) will the rider be at the bottom of the Ferris wheel?

e.How long does it take for the Ferris wheel to go through one rotation?

A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at its lowest position and takes 3.0 s to go from the top to the bottom and back again, determine an equation to model the data.

In 2001, Windsor, Ontario will receive its maximum amount of sunlight, 15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on December 21.

a) Due to the earth's revolution about the sun, the hours of daylight function is periodic. Determine an equation that can model the hours of daylight function for Windsor, Ontario.

b)On what day(s) can Windsor expect 13.5 hours of sunlight?

tan y =√2 , where x and y are acute angles, find the value of x if sin x = 1 - cos y

Two ships P and Q left a port R at the same time on different routes. Q sailed on a bearing of 150° while P sailed on the north side of Q.After a distance of 8km and 10 km by p anq respectively their distance apart was 12km. Find the bearing of P from R.

May someone help me with this HW problem?

The depth (D metres) of water in a harbour at a time (t hours) after midnight on a particular day can be modelled by the function
D = 2 sin(0.51t - 0.4) +5, t <=15,
where radians have been used.

Select the two options which are correct statements about the predictions based on this model.

Select one or more:
a) The smallest depth is 5 metres. 
b) At midday, the depth is approximately 7 metres. 
c) The model can be used to predict the tide for up to 15 days. 
d) The largest depth is 7 metres.
e) At midnight the depth is approximately 4.2 metres.
f) The time between the two high tides is exactly 12 hours. 
g) The depth of water in the harbour falls after midnight.