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mathematics
precalculus

Questions and Answers of Precalculus

Find the exact value of expression. sin cos
Find the exact value of expression. tan cot cot 3
Find the exact value of expression. 5п sin 4 cos
Find the exact value of expression. COS csc cos 2 2.
Find the exact value of expression. sec sin 2.
Find the exact value of expression. /3' 2 cos sin sin
Find the exact value of expression.sin[tan-1(-1)]
Find the exact value of expression.sec(tan-1 √3)
Find the exact value of expression.csc(tan-1 1)
Find the exact value of expression. cot sin 2,
Find the exact value of expression. sec sec cos 2.
Find the exact value of expression. tan sin 2,
Find the exact value of expression. V3 2 tan cos
Find the exact value of expression. sin n cos 2
Find the exact value of expression. cos sin 2
True or FalseThe domain of the inverse cotangent function is the set of real numbers.
True or Falsecsc-1 0.5 is not defined.
True or FalseIt is impossible to obtain exact values for the inverse secant function.
To find the inverse secant of a real number x such that |x| ≥ 1, convert the inverse secant to an inverse ________.
y = sec-1 x means _______, where |x| and ______ ≤ y ≤ _______, y ≠ π/2.
If tan θ = 1/2, -π/2 < θ < π/2, then sin θ = _______.
True or FalseThe graph of y = sec x is one-to-one on the interval [0, π/2) and on the interval (π/2, π].
Suppose that f(x) = 4x + 5 and g(x) = x2 + 5x – 24(a) solve f(x) = 0(b) solve f(x) = 13(c) solve f(x) = g(x) (d) solve f(x) > 0(e) solve g(x) ≤ 0(f) Graph y = f(x)(g) Graph y = g(x)
Solve log3( x + 8) + log3x = 2.
Solve 3x = 12. Round your answer to two decimal places
Analyze the graph of the rational function 2x – 7x – 4 R(x) x2 + 2x – 15 2.x 15
In the complex number system, solve the equation 3x5 – 10x4 + 21x3 – 42x2 + 36x – 8 = 0
Solve the triangle a = 20, c = 15, C = 40°
Sketch the graph of each of the following functions: (a) y = x (b) y = x2(c) y = √x (d) y = x3(e) y = ex(f) y = lnx(g) y = sinx(h) y = cosx(i) y = tanx
Graph each of the following functions on the interval [0, 4]: (a) y = ex(b) y = sinx(c) y = exsinx(d) y = 2x + sinx
If tanθ = -2 and 3π/2 < θ < 2π, find the exact value (a) sinθ (b) cosθ(c) sin(2θ)(d) cos(2θ)(e) sin(1/2 θ) (f) cos(1/2 θ)
Graph the function y = -2cos(2x - π).
Graph the function y = 3sin (πx).
Determine the domain of the function f (x) = Vx² – 3x-4 %3D
Find an equation for the circle with center at the point and (-5, 1) radius 3. Graph this circle.
Find the real solutions, if any, of the equation 3x2 + 1 = 4x.
Logan is playing on her swing. One full swing (front to back to front) takes 6 seconds and at the peak of her swing she is at an angle of 42° with the vertical. If her swing is 5 feet long, and we
The area of the triangle shown below is 54√2 square units; find the lengths of the sides. 5x 6x 7x
Given that is an isosceles triangle and the shaded sector is a semicircle, find the area of the entire region. Express your answer as a decimal rounded to two places. 40°
Madison wants to swim across Lake William from the fishing lodge (A) to the boat ramp (B), but she wants to know the distance first. Highway 20 goes right past the boat ramp and County Road 3 goes to
Find the area of the quadrilateral shown. 5/72 11
Find the area of the shaded region enclosed in a semicircle of diameter 8 centimeters. The length of the chord AB is 6 centimeters. 6. 8
A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to
A 12-foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground.What is the angle formed by the ground and the ladder?
Find the area of the triangle described in Problem 5. Data From problem 5. 8. 5 10
Find the area of the triangle described in Problem 8. Data From Problem 8a = 8, b = 4, C = 70°
Solve triangle.a = 8, b = 4, C = 70°
Solve triangle. a = 3, b = 7, A = 40°
Solve triangle.A = 55°, C = 20°, a = 4
use the given information to determine the three remaining parts of each triangle. 5 A. 10
use the given information to determine the three remaining parts of each triangle. 12 b. 22° 41°
Use the given information to determine the three remaining parts of the triangle. 17 a 52 19
Find the exact value of sin 40° - cos 50°.
Find the exact value of the six trigonometric functions of the angle θ in the figure. 3
Graph function. y = 2cos(2x) + sinx/2, x ≤ x ≤ 2π
Graph function. y = 2 sin x + cos(2x), , 0≤x ≤2π
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the
An object of mass m attached to a coiled spring with damping factor b is pulled down a distance a from its rest position and then released. Assume that the positive direction of the motion is up and
An object of mass m attached to a coiled spring with damping factor b is pulled down a distance a from its rest position and then released. Assume that the positive direction of the motion is up and
The distance d (in feet) that an object travels in time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its rest position? (c)
The distance d (in feet) that an object travels in time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its rest position? (c)
The distance d (in feet) that an object travels in time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its rest position? (c)
The distance d (in feet) that an object travels in time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its rest position? (c)
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, develop a model that relates the
Rework Problem 61 if the belt is crossed, as shown in the figure. 6.5 in. 2.5 in. 2 ft.-
The drive wheel of an engine is 13 inches in diameter, and the pulley on the rotary pump is 5 inches in diameter. If the shafts of the drive wheel and the pulley are 2 feet apart, what length of belt
The Majesty leaves the Port at Boston for Bermuda with a bearing of S80°E at an average speed of 10 knots. After 1 hour, the ship turns 90° toward the southwest. After 2 hours at an average speed
The irregular parcel of land shown in the figure is being sold for $100 per square foot. What is the cost of this parcel? 20 ft 50 ft 100 40° 100 ft
To approximate the area of a lake, Cindy walks around the perimeter of the lake, taking the measurements shown in the illustration. Using this technique, what is the approximate area of the
Two homes are located on opposite sides of a small hill. See the illustration. To measure the distance between them, a surveyor walks a distance of 50 feet from house P to point R, uses a transit to
A sailboat leaves St. Thomas bound for an island in the British West Indies, 200 miles away. Maintaining a constant speed of 18 miles per hour, but encountering heavy crosswinds and strong currents,
A highway whose primary directions are north–south is being constructed along the west coast of Florida.Near Naples, a bay obstructs the straight path of the road. Since the cost of a bridge is
Rebecca, the navigator of a ship at sea, spots two lighthouses that she knows to be 2 miles apart along a straight shoreline. She determines that the angles formed between two line-of-sight
Two observers simultaneously measure the angle of elevation of a helicopter. One angle is measured as 25°, the other as 40° (see the figure). If the observers are 100 feet apart and the helicopter
A straight trail with a uniform inclination leads from a hotel, elevation 5000 feet, to a lake in a valley, elevation 4100 feet. The length of the trail is 4100 feet. What is the inclination (grade)
From a glider 200 feet above the ground, two sightings of a stationary object directly in front are taken 1 minute apart (see the figure). What is the speed of the glider? 40 10° 200 ft ---
From a stationary hot-air balloon 500 feet above the ground, two sightings of a lake are made (see the figure). How long is the lake? 500 ft A 25° 65°
The Willis Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of Lake Michigan, as indicated in the figure on the following page. An observer in a pleasure boat on
Find the height of the building shown in the figure. 80 ft
Find the distance from A to C across the river illustrated in the figure. AA AÂM Â Âª 25° 50 ft
The hypotenuse of a right triangle is 12 feet. If one leg is 8 feet, find the degree measure of each angle.
Find the area of the segment of a circle whose radius is 6 inches formed by a central angle of 50°.
Find the area of the triangle.A = 10°, C = 40°, c = 3
Find the area of the triangle.A = 50°, B = 30°, a = 1
Find the area of the triangle.a = 3, b = 2, c = 2
Find the area of the triangle.a = 4, b = 2, c = 5
Find the area of the triangle.a = 10, b = 7, c = 8
Find the area of the triangle.a = 4, b = 3, c = 5
Find the area of the triangle.a = 2, b = 1, C = 100°
Find the area of the triangle.b = 4, c = 10, A = 70°
Find the area of the triangle.b = 5, c = 5, A = 20°
Find the area of the triangle.a = 2, b = 3, C = 40°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 1, b = 2, C = 60°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” c = 5, b = 4, A = 70°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 4, A = 20°, B = 100°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 3, A = 10°, b = 4
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 3, b = 2, c = 2
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 1, b = 1/2 , c = 4/3
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 2, b = 3, A = 20°

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