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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, find the absolute value of the given complex number. √2 – бі
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.a = 4, α = 60°,
For the following exercises, test the equation for symmetry. r = 5cos 3θ
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.γ =
What is De Moivre’s Theorem and what is it used for?
Why are there many sets of parametric equations to represent on Cartesian function?
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth. α = 43°,
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.α =
For the following exercises, graph each set of parametric equations by making a table of values. Include the orientation on the graph. [x(t) = t - 1 y(t) = t²
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 5-t y(t)=8-2t
For the following exercises, convert the given polar coordinates to Cartesian coordinates with r > 0 and 0 ≤ θ ≤2π. Remember to consider the quadrant in which the given point is located when
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .P1 =
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.α =
For the following exercises, test the equation for symmetry.r = 4
For the following exercises, graph each set of parametric equations by making a table of values. Include the orientation on the graph. x(t) = t³ |y(t)=t+2
For the following exercises, convert the given polar coordinates to Cartesian coordinates with r > 0 and 0 ≤ θ ≤2π. Remember to consider the quadrant in which the given point is located when
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. [x(t) = |y(t) = 2t² x(t) = 3t - 1
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Plot the point
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.b = 10, β =
Describe the three types of symmetry in polar graphs, and compare them to the symmetry of the Cartesian plane.
How do we find the product of two complex numbers?
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth. β = 50°,
What are the characteristics of the letters that are commonly used to represent vectors?
If you are looking for a missing side of a triangle, what do you need to know when using the Law of Cosines?
Find the area of the triangle in Figure 1. Round each answer to the nearest tenth. 6.25 7 Figure 1 5 60%
Assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve the triangle, if possible, and round each answer to the nearest tenth, given β = 68°, b = 21, c = 16.
What is a system of parametric equations?
What are two methods used to graph parametric equations?
How are polar coordinates different from rectangular coordinates?
How is a vector more specific than a line segment?
Describe the altitude of a triangle.
A complex number is a + bi. Explain each part.
If you are looking for a missing angle of a triangle, what do you need to know when using the Law of Cosines?
Which of the three types of symmetries for polar graphs correspond to the symmetries with respect to the x-axis, y-axis, and origin?
What is one difference in point-plotting parametric equations compared to Cartesian equations?
How are the polar axes different from the x- and y-axes of the Cartesian plane?
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth. α =
Some examples of a third parameter are time, length, speed, and scale. Explain when time is used as a parameter.
What are i and j, and what do they represent?
Explain what s represents in Heron’s formula.
What are the steps to follow when graphing polar equations?
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Solve the
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Find the area of
Explain how to eliminate a parameter given a set of parametric equations.
A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15° to the right of his original course, and flies 1 hour in the new direction. If he maintains a constant
Why are some graphs drawn with arrows?
Explain how polar coordinates are graphed.
When can you use the Law of Sines to find a missing angle?
How is a complex number converted to polar form?
What is component form?
Explain the relationship between the Pythagorean Theorem and the Law of Cosines.
Convert (2, 2) to polar coordinates, and then plot the point.
Name a few common types of graphs of parametric equations.
Describe the shapes of the graphs of cardioids, limaçons, and lemniscates.
What is a benefit of writing a system of parametric equations as a Cartesian equation?
How are the points (3,π/2) and (−3, π/2) related?
In the Law of Sines, what is the relationship between the angle in the numerator and the side in the denominator?
When a unit vector is expressed as 〈a, b〉, which letter is the coefficient of the i and which the j?
What part of the equation determines the shape of the graph of a polar equation?
When must you use the Law of Cosines instead of the Pythagorean Theorem?
Convert (2, π/3) to rectangular coordinates.
Why are parametric graphs important in understanding projectile motion?
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.A pilot is flying
Explain why the points (−3, π/2) and (3, −π/2) are the same.
What is a benefit of using parametric equations?
What type of triangle results in an ambiguous case?
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).sin2 x − 1 + 2 cos(2x) − cos2 x = 1
For the following exercises, find all solutions exactly to the equations on the interval [0,2π). sin(2x) sec² x
For the following exercises, find all solutions exactly to the equations on the interval [0,2π). sin(2x) 2 csc² x = 0
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).tan2 x − 1 − sec3 x cos x = 0
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).2cos2 x − sin2 x − cos x − 5 = 0
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).1/sec2 x + 2 + sin2 x + 4cos2 x = 4
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).An airplane has only enough gas to fly to a city 200 miles northeast of its current location. If the
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 15 feet long, what
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long, what
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A woman is watching a launched rocket currently 11 miles in altitude. If she is standing 4 miles from
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).An astronaut is in a launched rocket currently 15 miles in altitude. If a man is standing 2 miles from
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A woman is standing 8 meters away from a 10-meter tall building. At what angle is she looking to the
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A man is standing 10 meters away from a 6-meter tall building. Someone at the top of the building is
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A 20-foot tall building has a shadow that is 55 feet long. What is the angle of elevation of the sun?
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A 90-foot tall building has a shadow that is 2 feet long. What is the angle of elevation of the sun?
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A spotlight on the ground 3 meters from a 2-meter tall man casts a 6 meter shadow on a wall 6 meters
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).A spotlight on the ground 3 feet from a 5-foot tall woman casts a 15-foot tall shadow on a wall 6 feet
For the following exercises, find a solution to the word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.A person does a handstand
For the following exercises, find a solution to the word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.A person does a handstand
For the following exercises, find a solution to the word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.A 23-foot ladder is
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).3sec2 x + 2 + sin2 x − tan2 x + cos2 x = 0
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).sin2 x( 1 − sin2 x) + cos2 x( 1 − sin2 x) = 0
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).sin2 x − cos2 x − 1 = 0
For the following exercises, find all solutions exactly to the equations on the interval [0,2π).csc2 x − 3csc x − 4 = 0
For the following exercises, solve the equations algebraically, and then use a calculator to find the values on the interval [0,2π). Round to four decimal places.4sin2 x + sin(2x)sec x − 3 = 0
For the following exercises, solve the equations algebraically, and then use a calculator to find the values on the interval [0,2π). Round to four decimal places.2tan2 x + 9tan x − 6 = 0
For the following exercises, solve the equations algebraically, and then use a calculator to find the values on the interval [0,2π). Round to four decimal places.sin2 x − 2cos2 x = 0
For the following exercises, solve the equations algebraically, and then use a calculator to find the values on the interval [0,2π). Round to four decimal places.tan2 x − sec x = 1
For the following exercises, solve the equations algebraically, and then use a calculator to find the values on the interval [0,2π). Round to four decimal places.6tan2 x + 13tan x = −6
For the following exercises, solve the equations algebraically, and then use a calculator to find the values on the interval [0,2π). Round to four decimal places.tan2 x + 3tan x − 3 = 0
For the following exercises, use a calculator to find all solutions to four decimal places.cos x = 0.71
For the following exercises, use a calculator to find all solutions to four decimal places.tan x = −0.34
For the following exercises, use a calculator to find all solutions to four decimal places.sin x = −0.55
For the following exercises, use a calculator to find all solutions to four decimal places.sin x = 0.27

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