Trigonometry Answers

Using de Moivres theorem, express


Cos5A and sin4A as polynomials in sin A and cos A.

pls i need to know the diagram of this bearing of a village R is 10km from a point P on a bearing 025° from P. Another village A is 6km from P on a bearing 162°. Calculate (a) distance of R from A. (b) bearing of R from A

Let z = cosA + sinA


then z^n = cos(nA) + i sin(nA) for all n E N (by de Moivre) and z^-n = cos(nA) - i sin(nA).


1) show that 2cos(nA) = z^n + z^-n and 2i sin(nA) = z^n - z^-n.


2) show that 2^n cos^n A = ( z + 1/z)^n and (2i)^n sin ^n A= (z - 1/z)^n.


3) Use (2) to express sin^7 A in terms of multiple angles


4) Express cos^3 A sin ^4 A in terms of multiple angles


5) Eliminate A from the equations 4x = cos(3A) + 3cosA ; 4y = 3 sin A - sin (3A) .

An explorer standing from an island on the bearing of 125° at a distance of 100km. Show this diagram as it relative position of both the explorer and the island

Ross is downtown Toronto and wants to determine how tall the CN Tower is (without using his smartphone). Ross stands 750m from the base of the tower and holds a clinometer at 1.5 m height and sights the tip of the tower at an angle of 36°. How tall is the CN Tower?

[4 marks]

As the city planner of Right City, you are responsible to report information to help the Board of Supervisors make decisions about the budgets for the fire and police departments. The board has asked for a report with answers to the following questions. Each grid unit in the figure at right represents

1

mile.

For fire safety, bushes will be cleared along the perimeter of the city. What is the length of the perimeter? Include all of your calculations in your report.

Some people say that Right City got its name from its shape. Is the shape of the city a right triangle? Show how you can tell.

Using pencil, a pair of compass and ruler only, construct a hexagon in a circle of 60mm radius. Measure and write down the altitude

1)prove the identity (sin theta +cos theta)(1 - sin theta cos theta)= sin cube theta + cos

cube theta

2)hence solve the equation (sin theta + cos theta)(1- sin theta cos theta)=3 cos cube theta for 0 degree <=theta<=360 degree

Why do we need trigonometry formulas? Why is it important for us?