Trigonometry Answers

find the domain of the indicated functions.express answers in both interval notation and inequality notation.

f (x)=4-9x+3x²

translate each algebraic definition of the following function into a verbal definition.

f (x)=2x²⁺⁵

g (x)=-2x+7

M (x)=5t-2

solve the following equation for 0«x«360

a) 6 cos²x + sin x - 4

b) 9 tan x + tan²x + 5 sec² x - 3

given sin α = 3/5 and cos β = -4/5 , α is an acute angle and β is an obtuse angle find ;

a) cot α + cosec β

b) sin 2α tan 2β

A poster is to have an area of 180 in with 1-inch margins at the bottom and sides and a 2-inch margin at the top. What dimensions will give the largest printed area?

A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 300. At what rate is the distance from the plane to the radar station increasing a minute later?

A cone of radius 2 cm and height 5 cm is lowered point first into a tall cylinder of radius 7 cm that is partially filled with water. Determine how fast the depth of the water is changing at the moment when the cone is completely submerged if the cone is moving with a speed of 3 cm/s at that moment.

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.