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study help
mathematics
precalculus
Questions and Answers of
Precalculus
Draw, in standard position, the angle whose measure is given.2 rad
Find the value of the sum.
Find all solutions of the equation.2x2 - 2x + 1 = 0
Find the value of the sum.
Find all solutions of the equation.z2 + z + 2 = 0
Find the exact trigonometric ratios for the angle whose radian measure is given.3π/4
Find the value of the sum.
Find all solutions of the equation.z2 + 1/2z + 1/4 = 0
Find the exact trigonometric ratios for the angle whose radian measure is given.4π/3
Find the value of the sum.
Write the number in polar form with argument between 0 and 2π.-3 + 3i
Find the exact trigonometric ratios for the angle whose radian measure is given.9π/2
Find the value of the sum.
Write the number in polar form with argument between 0 and 2π.1 - √3i
Find the exact trigonometric ratios for the angle whose radian measure is given.-5π
Find the value of the sum.
Write the number in polar form with argument between 0 and 2π.3 + 4i
Find the exact trigonometric ratios for the angle whose radian measure is given.5π/6
Find the value of the sum.
Write the number in polar form with argument between 0 and 2π.8i
Identify the type of curve and sketch the graph. Do not plot points. Just use the standard graphs given in Figures 5, 6, 8, 10, and 11 and shift if necessary.x2 - y2 - 4x + 3 = 0
Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.z = √3 + i, w = 1 + √3i
Find the value of the sum.
Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.z = 4√3 - 4i, w = 8i
Identify the type of curve and sketch the graph. Do not plot points. Just use the standard graphs given in Figures 5, 6, 8, 10, and 11 and shift if necessary.y2 - 2x + 6y + 5 = 0
Find the remaining trigonometric ratios.sin a = 2, 0 < a < π/2
Find the value of the sum.
Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.z = 2√3 - 2i, w = -1 + i
Find the remaining trigonometric ratios.sec ф = -1.5, π/2 < ф < π
Find the value of the sum.
Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.z = 4(√3 + i), w = -3 - 3i
Identify the type of curve and sketch the graph. Do not plot points. Just use the standard graphs given in Figures 5, 6, 8, 10, and 11 and shift if necessary. 4x2 + 9y2 - 16x + 54y + 61 = 0
Find the remaining trigonometric ratios.cos x = -1/3. π < x < 3π/2
Find the value of the sum.
Find the indicated power using De Moivre’s Theorem.(1 + i )20
Sketch the region bounded by the curves.y = 3x, y = x2
Find the remaining trigonometric ratios.cot B = 3, π < B < 2π
Find the value of the sum.
Find the indicated power using De Moivre’s Theorem.(1 - √3 i )5
Sketch the region bounded by the curves.y = 4 - x2, x - 2y = 2
Find the remaining trigonometric ratios.csc θ = 3/5,
Find the value of the sum.
Find the indicated power using De Moivre’s Theorem.(2√3 + 2i)5
Find an equation of the parabola with vertex (1, -1) that passes through the points (-1, 3) and (3, 3).
Find, correct to five decimal places, the length of the side labeled x.
Find the number n such that
Find the indicated power using De Moivre’s Theorem.(1 - i)8
Find an equation of the ellipse with center at the origin that passes through the points (1, -10√2/3) and (-2, 5√5/3).
Find, correct to five decimal places, the length of the side labeled x.
Sketch the graph of the set.{(x, y) | x2 + y2 < 1}
Find the indicated roots. Sketch the roots in the complex plane.The eighth roots of 1
Find, correct to five decimal places, the length of the side labeled x.
Find the indicated roots. Sketch the roots in the complex plane.The fifth roots of 32
Sketch the graph of the set.{(x, y) | x2 + y2 . 4}
Find, correct to five decimal places, the length of the side labeled x.
Find the indicated roots. Sketch the roots in the complex plane.The cube roots of i
Sketch the graph of the set.{(x, y) | y > x2 - 1}
Prove each equation.(a) Equation 10a (b) Equation 10b
Prove formula (e) of Theorem 3 using the following method published by Abu Bekr Mohammed ibn Alhusain Alkarchi in about ad 1010. The figure shows a square ABCD in which sides AB and AD have been
Find the indicated roots. Sketch the roots in the complex plane.The cube roots of 1 + i
Sketch the graph of the set.{(x, y) | x2 + 4y2 < 4}
Evaluate each telescoping sum. (a) (b) (c) (d)
Write the number in the form a + bi.eiπ/2
Prove the generalized triangle inequality:
Write the number in the form a + bi.e2πi
Prove the identity.cos (π/2 - x) = sin x
Find the limit.
Write the number in the form a + bi.eiπ/3
Prove the identity.sin (π/2 + x) = sin x
Find the limit.
Write the number in the form a + bi.e-iπ
Prove the identity.sin (π - x) = sin x
Find the limit.
Write the number in the form a + bi.e2+iπ
Prove the identity.sin θ cot θ = cos θ
Write the number in the form a + bi.eπ+i
Prove the identity.(sin x + cos x)2 = 1 + sin 2x
Prove the identity.sec y - cos y = tan y sin y
Use Euler’s formula to prove the following formulas for cos x and sin x:cos x = eix + e-ix/2sin x = eix - eix/2i
Prove the identity.tan2a - sin2a = tan2a sin2a
If u(x) = f (x) + it(x) is a complex-valued function of a real variable x and the real and imaginary parts f (x) and g(x) are differentiable functions of x, then the derivative of u is defined to be
Prove the identity.tan 2θ = 2 tanθ/1 - tan2θ
Prove the identity.cot2θ + sec2θ = tan2θ + csc2θ
Prove the identity.2 csc 2t = sec t csc t
Prove the identity.1/1 - sin θ + 1/1 + sin θ = 2 sec2θ
Prove the identity.sin x sin 2x + cos x cos 2x = cos x
Prove the identity.sin2x - sin2y = sin(x + y) sin(x - y)
Prove the identity.sin ф/1 - cos ф = csc ф + cot ф
If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression.sin(x + y)
If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression.cos(x + y)
If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression.cos(x - y)
If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression.sin(x - y)
If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression.sin 2y
If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression.cos 2y
Find all values of x in the interval [0, 2π]that satisfy the equation.2 cos x - 1 = 0
Find all values of x in the interval [0, 2π]that satisfy the equation.3 cot2x = 1
Find all values of x in the interval [0, 2π] that satisfy the equation.2 sin2x = 1
Find all values of x in the interval [0, 2π] that satisfy the equation.|tan x | = 1
Find all values of x in the interval [0, 2π] that satisfy the equation.sin 2x = cos x
Find all values of x in the interval [0, 2π] that satisfy the equation.2 cos x + sin 2x = 0
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