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mathematics
precalculus

Questions and Answers of Precalculus

Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.tan[tan-15]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.cos[cos-1(-0.3)]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.cos(cos-10.6)
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.sin(sin-10.09)
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.sin-1[sin(-8π/9)]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.cos-1[cos(15π/7)]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.sin-1[sin(-π/8)]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.tan-1[tan(2π/3)]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.cos-1[cos(3π/4)]
Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.sin-1[sin(3π/8)]
Find the exact value of the expression. Do not use a calculator.cot-1(-1)
Find the exact value of the expression. Do not use a calculator.sec-1√2
Find the exact value of the expression. Do not use a calculator.tan-1(-√3)
Find the exact value of the expression. Do not use a calculator.cos-1 (-√3/2)
Find the exact value of the expression. Do not use a calculator.sin-1(-1/2)
Find the exact value of the expression. Do not use a calculator.tan-11
Find the exact value of the expression. Do not use a calculator.cos-10
Find the exact value of the expression. Do not use a calculator.sin-11
Derive formula (9).
Derive formula (8).
Derive formula (7).
Derive formula (3).
If α + β + γ show that tanα + tanβ + tanγ = tanα tanβ tanγ
If α + β + γ show that sin(2α) + sin(2β) + sin(2γ) = 4 sinα sinβsinγ
The range R of a projectile propelled downward from the top of an inclined plane at an angle to the inclined plane is given byWhere is the initial velocity of the projectile, is the angle the plane
The moment of inertia I of an object is a measure of how easy it is to rotate the object about some fixed point. In engineering mechanics, it is sometimes necessary to compute moments of inertia with
(a) Write the sound emitted by touching the # key as a product of sines and/or cosines.(b) Determine the maximum value of y.(c) Graph the sound emitted by touching the # key.
On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two tones, given byy = sin(2πlt) and
Solve each equation on the interval 0 ≤ θ < 2π.sin(4θ) - sin(6θ) = 0
Solve each equation on the interval 0 ≤ θ < 2π.cos(4θ) - cos(6θ) = 0
Solve each equation on the interval 0 ≤ θ < 2π.cos(2θ) + cos(4θ) = 0
Solve each equation on the interval 0 ≤ θ < 2π.sin(2θ) + sin(4θ) = 0
Establish each identity.1 - cos(2θ) + cos(4θ) -cos(6θ) = 4sinθcos(2θ)sin(3θ)
Establish each identity.1 + cos(2θ) + cos(4θ) + cos(6θ) =4 cosθcos(2θ)cos(3θ)
Establish each identity. a + B sin a – sin B -cot 2 - cos B ccos a
Establish each identity. sin a + sin ß tan cos a + cos B 2.
Establish each identity. cos a + cos B cos a – cos B cot 2 = -cot
Establish each identity. sin a + sin ß cot = tan sin a – sin B
Establish each identity. cos(40) – cos(80) tan(20) tan(60) cos(40) + cos(80)
Establish each identity. sin(40) + sin(80) tan(60) sin(40) – sin(80) tan(20)
Establish each identity. sin(40) – sin(80) cos(40) – cos(80) -cot(60)
Establish each identity. sin(40) + sin(80) cos(40) + cos(80) tan(60)
Establish each identity.sinθ [3sin(3θ) + sin(5θ)] = cosθ[3cos(3θ) - cos(5θ)]
Establish each identity.sinθ [sinθ + sin(3θ)] = cosθ[cosθ - cos(3θ)]
Establish each identity. cos 0 – cos(50) sin 0 + sin(50) tan(20)
Establish each identity. |cos 0 – cos(30) sin 0 + sin(30) tan 0
Establish each identity. cos 0 – cos(360) sin(30) – sin 0 tan(20)
Establish each identity. sin(40) + sin(20) cos(40) + cos(20) tan(30) COS
Establish each identity. cos 0 + cos(30) 2 cos(20) cos 0 =
Establish each identity. sin 0 + sin(30) 2 sin(20) = cos 0
Express each sum or difference as a product of sines and/or cosine.sinθ/2 - sin3θ/2
Express each sum or difference as a product of sines and/or cosine.cosθ/2 - cos3θ/2
Express each sum or difference as a product of sines and/or cosine.cosθ + cos(3θ)
Express each sum or difference as a product of sines and/or cosine.sinθ + sin(3θ)
Express each sum or difference as a product of sines and/or cosine.cos(5θ) - cos(3θ)
Express each sum or difference as a product of sines and/or cosine.cos(2θ) + cos(4θ)
Express each sum or difference as a product of sines and/or cosinesin(4θ) + sin(2θ)
Express each sum or difference as a product of sines and/or cosine.sin(4θ) - sin(2θ)
Express each product as a sum containing only sines or only cosines.sinθ/2 cos5θ/2
Express each product as a sum containing only sines or only cosines.sin3θ/2 cosθ/2
Express each product as a sum containing only sines or only cosines.cos(3θ) cos (4θ)
Express each product as a sum containing only sines or only cosines.sinθsin(2θ)
Express each product as a sum containing only sines or only cosines.sin(4θ) cos(6θ)
Express each product as a sum containing only sines or only cosines.sin(3θ) sin(5θ)
Express each product as a sum containing only sines or only cosines.sin(4θ) cos(2θ)
Express each product as a sum containing only sines or only cosines.cos(4θ) cos(2θ)
Express each product as a sum containing only sines or only cosines.sin(4θ) sin(2θ)
Find the exact value of each expression.sin 255° - sin 15°
Find the exact value of each expression.cos 255° - cos 195°
Find the exact value of each expression.sin 75° + sin 15°
Find the exact value of each expression.sin 285° • sin 75°
Find the exact value of each expression.cos 285° • cos 195°
Find the exact value of each expression.sin 195° • cos 75°
If tan θ = a tan θ/3, express tan θ/3 in terms of a.
Show that sin(30) 4 sin 0 + sin°(0 + 120°) + sin°(0 + 240°) -
Show thatand use it to find sin π/16 and cos π/16. V2 + V2 Cos 2 ||
Use the fact thatto find sin π/24 and cos π/24. TT cos 12 i(Võ + 4 ||
Repeat Problem 107 for g(x) = cos2 x.Data from problem 107GraphFor 0 ≤ x ≤ 2π by using transformations. 1 - cos(2x) f(x) = sin². 2.
GraphFor 0 ≤ x ≤ 2π by using transformations. 1 - cos(2x) f(x) = sin². 2.
If z = tan α/2 , show that cos α = 1 – z2/1 + z2.
If z = tan α/2, show that sin α = 2z/1 + z2.
Find the value of the number C: cos² x + C = cos(2x) 4
Find the value of the number C: - sin² x + C = - cos(2x) 4
If x = 2 tan θ, express cos(2θ) as a function of x.
If x = 2 tan θ, express sin(2θ) as a function of x.
A rectangle is inscribed in a semicircle of radius 1. See the illustration. (a) Express the area A of the rectangle as a function of the angle θ shown in the illustration.(b) Show that A(θ) =
Show that the area A of an isosceles triangle whose equal sides are of length s and θ is the angle between them isSee the illustration. The height h bisects the angle θ and is the perpendicular
An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes. A first approximation to the sawtooth curve is given
An object is propelled upward at an angle θ, 45° < θ < 90°, to the horizontal with an initial velocity of υ0 feet per second from the base of a plane that makes an angle of 45°with the
The product of inertia for an area about inclined axes is given by the formulaShow that this is equivalent to Iy(cos² 0 – sin²0) Iuw = I, sin 0 cos 0 – I, sin 0 cos 0 + I xy(cos² 0 – sin? 0)
In a laser projection system, the optical or scanning angle θ is related to the throw distance D from the scanner to the screen and the projected image width W by the equation (a) Show that the
A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. See the illustration. The area A of
Find the real zeros of trigonometric function on the interval 0 ≤ θ ≤ 2π.f(x) = cos(2x) + sin2 x
Find the real zeros of trigonometric function on the interval 0 ≤ θ ≤ 2π.f(x) = cos(2x) + cos x
Find the real zeros of trigonometric function on the interval 0 ≤ θ ≤ 2π.f(x) = sin(2x) - sin x
Find the exact value of expression. csc 2 sin 5,
Find the exact value of expression. -1 sec 2 tan 4.
Find the exact value of expression. - sin cos
Find the exact value of expression. sin? SI cos 5,
Find the exact value of expression. cos 2 tan 3 3

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