Trigonometry Answers

P(3,-3) lies on the terminal arm of an angle in standard position.

a. Draw a sketch of the principal angle (θ) in standard position. Label θ AND the related acute

angle, RA. [2 marks]

b. Determine the exact primary trig ratios for θ. Show ALL your work. You do not need to

rationalize the denominator, but you must simplify your radical and your ratios. [5 marks]

c. Determine the values of the principal angle and related acute angle to the nearest degree.

1. A commercial ship is heading due North

at 12.0 km/hr but drifts westward at 5.0

km/hr. determine the magnitude and

direction of the resultant velocity of the

ship.

2. Find the resultant of the following

vectors.

A = 30 m at 30° with the x-axis

B = 20 m at 120° with the x-axis

C = 10 m at 225° with the x-axis.

Show that d= 2v² costheta sintheta(0_x)/gcos²thetax

Find the length of an arc in a circle of radius 10 centimeters subtended by the central angle of 50°. Show your work.

2. Graph on [-4π, 4π] and verbalize how the graph varies from the graphs of . 

Graph  on the window [−5π, 5π] and describe freely what the graph shows. You can use www.desmos.com/calculator to obtain the graphs.

3. A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach up the side of the building? Show the steps of your reasoning.  

if the side of triangle are 16,20 and 27 respectivly,what is the lenght of the bisector of the largest angle?

7.Two ships leave a dock at the same time. One sails northeast at the rate of 8.5 miles an hour, the other sails north at the rate of 10 miles an hour. How far apart are they at the end of 2 hours?

8. If the slower ship in the preceding exercise leaves at noon, and the other at 1 p.m., how far apart are they at 2 p.m.? 9. The diagonals of a parallelogram are 7 inches and 9 inches respectively; they intersect at an angle of 52°. Find the sides of the parallelogram.

10. A military observer notes two enemy batteries which sub tend, at his observation post, an angle of 40°. The interval between the flash and the report of a gun is 5 seconds for one battery, and 4 seconds for the other. If the velocity of sound is 1140 feet a second, how far apart are the batteries?

Find the height of a trapezoid with area of 99m2 and the bottom base is twice the top base, which measures 6m.

His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground. 

At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.

 ____________ feet 

Marco would like to hang a banner over his shoe store. He has two ladders and would like to know high above the ground each ladder will allow him to place the banner.

His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground. 

At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.

 ____________ feet 

A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _______ feet.

Explain how you determined your answer (explain all work used to determine the answer).

Find the angle that the 15-foot ladder makes with the building. Round your answer to the nearest tenth. ____________ degrees

The 15-foot ladder makes a ________ degree angle with the building.

Explain and show the work you used to solve the problem. Justify the answer you have.

Will the 13-foot ladder make the same angle with the building? Justify your reasoning.

If Cot θ= 12/5 , and

Cos θ= 1/tan θ. Evaluate;

Cos2θ/sin θ + Cos θ