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mathematics
precalculus

Questions and Answers of Precalculus

Find the exact value of expression. sin 2 cos 5
Find the exact value of expression. tan 2 tan 4 4,
Find the exact value of expression. 3 tan 2 cos 5
Find the exact value of expression. cos 2 cos 5
Find the exact value of expression. cos 2 sin 5. COS
Find the exact value of expression. V31 sin 2 sin 2
Find the exact value of expression. sin 2 sin 2
Solve equation on the interval 0 ≤ u ≤ 2π.tan(2θ) + 2 cos θ = 0
Solve equation on the interval 0 ≤ u ≤ 2π.tan(2θ) + 2 sin θ = 0
Solve equation on the interval 0 ≤ u ≤ 2π.cos(2θ) + 5 cos θ + 3 = 0
Solve equation on the interval 0 ≤ u ≤ 2π.3 - sin θ = cos(2θ)
Solve equation on the interval 0 ≤ u ≤ 2π.cos(2θ) + cos(4θ) = 0
Solve equation on the interval 0 ≤ u ≤ 2π.sin(2θ) + sin(4θ) = 0
Solve equation on the interval 0 ≤ u ≤ 2π.sin(2θ) = cos θ
Solve equation on the interval 0 ≤ u ≤ 2π.cos(2θ) = cos θ
Solve equation on the interval 0 ≤ u ≤ 2π.cos(2θ) = 2 - 2 sin2 θ
Solve equation on the interval 0 ≤ u ≤ 2π.cos(2θ) + 6 sin2 θ = 4
Establish identity. |In |cos e| =(In |1 + cos(20)| – In 2)
Establish identity. In |sin 0| = (In |1 – cos(20)| – In 2)
Establish identity.tan θ + tan(θ + 120°) + tan(θ + 240°) = 3 tan(3θ)
Establish identity. 3 tan 0 – tan 0 1 - 3 tan? 0 tan(30)
Establish identity. cos 0 + sin 0 cos 0 – sin 0 sin 0 2 tan(20) cos 0 cos e + sin 0
Establish identity. sin(30) sin 0 cos(30) = 2 cos 0
Establish identity. sin 0 + cos' 0 sin(20) .3 sin 0 + cos 0
Establish identity. 1 - tan cos e 1 + tan?
Establish identity. tan csc v – cot v ||
Establish identity. sec v + 1 sec v – 1 cot
Establish identity. 2 1 - cos 0 csc2
Establish identity. sin? 0 cos? 0 1 – cos(40)] [
Establish identity. cos(20) 1 + sin(20) cot 0 - 1 cot 0 + 1
Establish identity.(4 sinu cosu)(1 - 2 sin2u) = sin(4u)
Establish identity.cos2(2u) - sin2 (2u) = cos(4u)
Establish identity. csc(20) sec 0 csc 0 SC
Establish identity. sec e 2 – sec? e sec(20)
Establish identity. cot(20) tan 0) 5(cot 0
Establish identity. cot? 0 – 1 cot(20) 2 cot 0
Establish identity. cot 0 – tan 0 cot 0 + tan 0 cos(20)
Establish identity.cos4 θ - sin4 θ = cos(2θ)
Find an expression for cos(5θ) as a fifth-degree polynomial in the variable cos θ.
Find an expression for sin(5θ) as a fifth-degree polynomial in the variable sin θ.
Develop a formula for cos(4θ) as a fourth-degree polynomial in the variable cos θ.
Develop a formula for cos(3θ) as a third-degree polynomial in the variable cos θ.
Show that sin(4θ) = (cos θ)(4 sin θ - 8 sin3 θ).
Show that sin4 θ = 3/8 – 1/2 cos(2θ) + 1/8 cos(4θ).
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.h(2α) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.h(α/2) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.g(α/2) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.f(α/2) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.f(2α) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.g(2α) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.h(θ/2) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.h(2θ) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.f(θ/2) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.g(θ/2) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.g(2θ) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the figures to evaluate the function given that f(x) = sin x, g(x) = cos x, and h(x) = tan x.f(2θ) х2 + у2 %3D 1 х2 + у2 %3D5 (a, 2). (-4, b)
Use the Half-angle Formulas to find the exact value of expression.cos (-3π/8)
Use the Half-angle Formulas to find the exact value of expression.sin (-π/8)
Use the Half-angle Formulas to find the exact value of expression.csc 7π/8
Use the Half-angle Formulas to find the exact value of expression.sec 15π/8
Use the Half-angle Formulas to find the exact value of expression.sin 195°
Use the Half-angle Formulas to find the exact value of expression.cos 165°
Use the Half-angle Formulas to find the exact value of expression.tan 9π/8
Use the Half-angle Formulas to find the exact value of expression.tan 7π/8
Use the Half-angle Formulas to find the exact value of expression.cos 22.5°
Use the Half-angle Formulas to find the exact value of expression.sin 22.5°
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2cot θ = 3, cos θ < 0
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2tan θ = -3, sin θ < 0
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2sec θ = 2, csc θ < 0
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2cot θ = -2, sec θ < 0
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2csc θ = -√5, cos θ < 0
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2sec θ = 3, sin θ > 0
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2 Уз Зп /3 < 0 < 27 sin 0 * 3
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2 V6 TT cos e 3
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2 Зт tan 0 2' 2
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2 4
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2 cos 0 5'
Use the information given about the angle θ, 0 ≤ θ ≤ 2π to find the exact value of(a) sin(2θ)(b) cos(2θ)(c) sin θ/2(d) cos θ/2 3 0 < 0 < - 5' TT sin 0 2
True or Falsetan(2θ) + tan(2θ) = tan(4θ)
True or Falsesin(2θ) has two equivalent forms:2 sin θ cos θ and sin2 θ - cos2 θ
Fill in the blanktan θ/2 = 1 – cos θ/ ____.
Fill in the blanksin2 θ/2 = ______ /2.
cos(2θ) = cos2 θ - ________ = _________ - 1 = 1 - ______.
Explain why formula (7) cannot be used to show thatEstablish this identity by using formulas (3a) and (3b). = cot 0 tan
Discuss the following derivation: tan 0 TT tan 0 + tan tan n(a -) - tan 0 + -cot 0 2 0 - tan 0 -tan 0 tan 0 tan tan 0 tan 2 티2
If tan α = x + 1 and tan β = x - 1, show that2 cot(α – β) = x2
If α + β + γ = 180° andcot θ = cot α + cot β + cot γ, 0 < θ < 90°show thatsin3 θ = sin(α - θ) sin(β - θ) sin(γ – θ)
Let L1 and L2 denote two nonvertical intersecting lines, and let θ denote the acute angle between L1 and L2 (see the figure). Show that where m1 and m2 are the slopes of L1 and L2,
In an alternating current (ac) circuit, the instantaneous power p at time t is given byShow that this is equivalent top(t) = Vm Im, sin(ωt) sin(ωt – φ) o sin²(@t) – V mlm sin o sin(@t)
One, Two, Three(a) Show that tan(tan-1 1 + tan-1 2 + tan-1 3) = 0.(b) Conclude from part (a) thattan-1 1 + tan-1 2 + tan-1 3 = π
Show that the difference quotient for f(x) = cos x is given by
Show that the difference quotient for f(x) = sin x is given by f(x + h) - f(x) sin(x + h) – sin x 1- cos h sin x sin h = Cos X
Show that cos(sin-1 υ + cos-1 υ) = 0.
Show that sin(sin-1 υ + cos-1 υ) = 1.
Show that cot-1 eυ = tan-1 C-υ.
Show that tan-1 (1/υ) = π/2 – tan-1 if υ > 0.
Show that tan-1 υ + cot υ = π/2.
Show that sin-1 υ + cos-1 υ = π/2.
Solve equation on the interval 0 ≤ θ ≤ 2π.cot θ + csc θ = -√3
Solve equation on the interval 0 ≤ θ ≤ 2π.tan θ + √3 = sec θ

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