Trigonometry Answers

We want to build a greenhouse that has a half cylinder roof of radius r and height r mounted horizontally on top of four rectangular walls of height h as shown in the figure. We have 200π m² of plastic sheet to be used in the construction of this structure. Find the value of r for the greenhouse with the largest possible volume we can build.

A pool, like the one in front of the Faculty of Science Building A, loses water from its sides and its bottom due to seepage, and from its top due to evaporation. For a pool with radius R and depth H in meters, the rate of this loss in m³/hour is given by an expression of the form aR² + bR²h + cRh².

where h is the depth of the water in meters, and a, b, c are constants independent of R, H and h. Due to this loss, water must be pumped into the pool to keep it at the same level even when the drains are closed. Suppose that a = 1/300 m/hour and b = c = 1/150 1/hour. Find the dimensions of the pool with a volume of 45π m³ which will require the water to be pumped at the slowest rate to keep it completely full.

Prove

tan(x) . Cos(x) =sin(x)

A sign with a mass of 10 kg is hung using two cables. The tension in cable A is 85N & the tension in cable B is 97N. Cable A makes an angle of 23 degree with the ceiling. Determine the angle that Cable B makes with the ceiling. Include a diagram to support your solution. Round your answer to 1 decimal place.

Solve for θ to the nearest hundredth, where 0 ≤ x ≤ 2π. a) 3 tan2 θ – 2 tan θ = 1

Find the exact value of the sum and cosine functions if angle θ is in standard position with the given coordinates of the terminal side.

1.) (3,4)

2.) (-2,2)

Angle θ is in standard position and lies in the given quadrant. When sin and cos θ is given, find the exact value of sin θ and cos θ.

1.) sin θ =½ ; Q1

2.) cos θ= -⅚; Q11

given sin x = 3/5 and cos y = -4/5 , x is an acute angle and y is and obtuse angle . find :

a)cot a + cos ec y

b)sin 2x + tan 2y

solve the following equation for 0<x<360

a) 6cos² x + sin x - 4

b)9 tan x + tan² x = 5 sec² x - 3

You were playing fetch with your dog and accidentally 

threw the toy and it got stuck on the roof of your 

house. You leaned the ladder against your house at a 

30° angle of elevation. The foot of the ladder is 7 feet 

from the foot of the house. How long is your ladder? 

Find the other angle and sides of the triangle:

1. Right triangle ABC with angle b=38° of side a=14 cm.
2. Obtuse triangle DEF with sides d=12, e=16.3 cm, f=13.5 cm