|
Without using a calculator, find:csc(x), sec(x) and cot(x) given:sin(x)=3/5, 0≤x≤π/2 csc(x) = cot(x)= sec(x)= How many times do the graphs of f(x) = sec(x) and g(x) = -kcos(x), where k is a positive constant, intersect on the interval 0≤x≤2π? 0 1 2 3 Give the coordinates of the circle's center and it radius. Radius: Center : x2 + y2 - 4x + 18y + 84 = 0 Write your answer in a coordinate form e.g.(1,2) A Find the graph of the equation below: x2-10x+y2=-9 B C Find the standard form of the equation of the parabola with the focus (0, 7) and vertex at the origin. y2=28x x2=28y y2=7x x2=7y Find the focus of the parabola.Write your answer in a coordinate form using improper fractions when necessary, e.g. (-7/6,4/3). Find the equation of the parabola with vertex at (5, 4) and focus at (-3, 4). ( place the + or - sign in front of the number in the box) (y )2= (x ) Give your answers in a coordinate form e.g. (1,2) Find the center and vertices of the ellipse. 4x2 + 9y2 − 24x + 72y + 144 = 0 Center Vertices (from left to the right) : Identify conic given by the equation below: 11x2 − 25y2 + 22x + 250y − 889 = 0 a circle a parabola an ellipse a hyperbola y=± Find the equations of the asymptotes of the hyperbola. 9y2 − 16x2 = 144 x A Find the graph of the following ellipse: 9x2 + 16y2 − 36x − 64y =44 B C A doorway in a castle is shaped like a parabola.Given that is 4 feet across and 8 feet high in the center,determine the width of the doorway at a point 5 feet off the ground.Round your answer to 2 decimal places. ( Hint: find the equation of the parabola) ft ( An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. Write an equation for the ellipse if the x-axis coincides with the water level and the y-axis passes through the center of the arch. )2 + ( )2=1 0 1 2 4 Determine how many places the following 2 conic intersect at. x2 + y2 = 345x2 - 3y2 = 180 Find the equation of the directrix of the parabola: Write your answer in an equation form without space, e.g. y=-7 or x=77 equation of the directrix: x = -1 4 (y + 8)2 + 2 Find eccentricity of the conic section below: x2 + y2 + 4x + 8y + 11 = 0 -π≤x≤π -π/2≤x≤π/2 0≤x≤π 0≤x≤2π For what restricted domain of y=tan(x) is y=arctan(x) the inverse function? Find the equation of the function represented in the graph below: y=cot(x) y=cot(x-π/4) y=tan(x-π/4) y=tan(x-π/2) Find the period of the function below. Give your answers in terms of π. period = π Find b given that y=cos(bx) has a period 2π/3 b= State the maximum and minimum values of: a) y= -cos(2x)+3 b) y=1+2sin(x-π/3) Max: Max: Min: Min: (Write your answer in a decimal form.) degrees Simplify the expression to a constant: (sinx)(csc(-x)) tan(x) -tan(x) csc(x) sec(x) The graph of y = cot(x) can be obtained by a horizontal shift of the graph of y = The graph of y = csc(x) has the same set of asymptotes as the graph of y = sin(x) tan(x) cot(x) csc(x) Match the graph with its equation by writing the color(R,B,G) y=sec(2x) y=sec(1/2x) y=1/2sec(x) |