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mathematics
precalculus

Questions and Answers of Precalculus

In Problems 15–29, 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-¹0.9)
In Problems 9–20, use the information given about the angle θ, 0 ≤ θ < 2π, to find the exact value of: (a) sin(20) (b) cos(20) (c) sin (d) cos 2 (e) tan(20) (f) tan-
In Problems 21–28 use sum, difference, product, or half-angle formulas to find the exact value of each expression.tan75°
In Problems 17–24, express each sum or difference as a product of sines and/or cosines. cos (50) cos(30)
In Problems 17–24, express each sum or difference as a product of sines and/or cosines. sin+sin (30)
In Problems 9–20, use the information given about the angle θ, 0 ≤ θ < 2π, to find the exact value of: (a) sin(20) (b) cos(20) NIO (c) sin- sin 2 (d) COS 0 2 (e) tan(20) (f) tan-
In Problems 15–29, 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)
In Problems 15–29, 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]
In Problems 17–24, express each sum or difference as a product of sines and/or cosines. cose+cos (30)
In Problems 15–29, 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(-1.6)]
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression. 7π 8 tan-
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression. 9π tan- 8
In Problems 21–28 use sum, difference, product, or half-angle formulas to find the exact value of each expression. 335 sin(cos-1
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression.sin 22.5°
In Problems 17–24, express each sum or difference as a product of sines and/or cosines. 0 cos 2 30 cos- 2
In Problems 15–29, 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(cos2 2π 3
In Problems 17–24, express each sum or difference as a product of sines and/or cosines. 0 sin- 2 30 sin- 2
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression.cos 22.5°
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression.cos165°
In Problems 15–29, 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. 3) sec tan-1. 3
In Problems 25–42, establish each identity. sin (40) + sin(20) cos(40)+cos (20) = tan (30)
In Problems 25–42, establish each identity. cos- cos (30) sin (30) sin tan (20)
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression. 7π 8 csc-
In Problems 15–29, 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. 314 sin cot-1;
In Problems 15–29, 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[sin-¹(-1)]
In Problems 25–42, establish each identity. cose - cos (30) = tane sin+sin (30)
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression. sin(-)
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression. cos 32 8
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 29–33, solve each equation on 0 ≤ θ < 2π. 4 sin² 03 0 =
In Problems 21–28 use sum, difference, product, or half-angle formulas to find the exact value of each expression.cos65°cos20° + sin65°sin20°
In Problems 30 and 31, find the inverse function f−1 of each function f. Find the range of f and the domain and range of f−1. f(x) = 2 sin (3x) 56 - VI sis VI
In Problems 29–33, solve each equation on 0 ≤ θ < 2π. -3 cos(-) = 0) tane
In Problems 25–42, establish each identity. cos(50) cos sin + sin(50) 0 tan (20)
In Problems 30 and 31, find the inverse function f−1 of each function f. Find the range of f and the domain and range of f−1. f(x) = —cosx+30SXST
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 29–33, solve each equation on 0 ≤ θ < 2π. cos² + 2 sin cos0 sin² 0 = 0 -
In Problems 25–42, establish each identity. sin [sin+sin (30)] = cos [cos - cos(30)]
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 25–42, establish each identity. sin 0 [sin (30) + sin(50)] = cos 0 [cos (30) cos (50)]
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 25–42, establish each identity. sin (40) + sin(80) cos(40)+cos (80) tan (60)
In Problems 29–33, solve each equation on 0 ≤ θ < 2π. sin (0+1)= cose
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 34–50, establish each identity. tan cotsin² 0 = cos²0
In Problems 34–50, establish each identity. cos cos sin 0 1 1 tan 0
In Problems 29–33, solve each equation on 0 ≤ θ < 2π. 4 sin ²0 + 7 sin0 = 2
In Problems 25–42, establish each identity. sin (40) + sin(80) sin (40) sin(80) tan (60) tan (20)
In Problems 25–42, establish each identity. sin a + sin 3 sin 3 sina - = tan +3 2 cot a - B 2
In Problems 32 and 33, write each trigonometric expression as an algebraic expression in u.cos(sin−1 u)
In Problems 34–50, establish each identity. csc 0 1 + csc0 1 sin cos²0
In Problems 32 and 33, write each trigonometric expression as an algebraic expression in u.tan(csc−1 u)
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 34–50, establish each identity. 5 cos² 0+3 sin² 0 = 3+ 2 cos²0
In Problems 25–42, establish each identity. sin (40) cos(40) sin(80) cos(80) -cot (60)
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 34–50, establish each identity. sin² 0(1+ cot20) = 1
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 34–50, establish each identity. 1 cos 0 sin + sin 0 1 - cose 2 csc 0
In Problems 25–42, establish each identity. cos (40) cos(80) cos(40)+cos (80) tan (20) tan (60)
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 25–42, establish each identity. cosa + cosß Cosa - cosß ota + cot ß₁ a - B 2 2 -cot
In Problems 25–42, establish each identity. sin a + sin ß cosa + cos 3 B a + ß 2 = tan-
In Problems 34–50, establish each identity. csc sin = cos cot
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 25–42, establish each identity. sin a cosa sin 3 cos 3 a + ß 2 =-cot-
In Problems 31–42, f (x) = sin x, g(x) = cos x, and h (x) = tan x. Use the figures below to evaluate each function. (a, 2) y x2 + y2 = 5 X (-1, b) x2 + y² = 1 α X
In Problems 25–42, establish each identity. 1 + cos(20) + cos(40) + cos(60) = 4 cos@cos(20) cos(30)
In Problems 34–50, establish each identity. 1 - 2 sin ²0 sin 0 cos cot - tan
In Problems 25–42, establish each identity. 1 cos(20) + cos(40) cos(60) = 4 sin cos(20)sin (30) - -
In Problems 34–50, establish each identity. 1 sin 0 sec 0 cos³0 1 + sin 0
In Problems 34–50, establish each identity. cos(a + 3) cosa sin ß cot 3 tan a
In Problems 34–50, establish each identity. cos(a + 3) cosa sin ß cot 3 tan a
In Problems 34–50, establish each identity. cos(a - ß) B) cosa cos 3 || 1+ tanatan 3
Show that sin ²0 cos 40 = + cos (20) - 16 32 -cos (40) - 16 -cos(60). 32
In Problems 43–48, use the figures to evaluate each function if f (x) = sin x, g(x) = cos x, and h(x) = tan x. x² + y² = 4 y a (x, 1) X x² + y² = 1 В (3₁) X
In Problems 34–50, establish each identity. 0 (1 + cos0) tan- tan== 2 sin 0
Show that cos60 5 16 + 15 -cos (20) + 32 3 -cos (40) + 16 -cos(60). 32
Show that sin 60 = 16 1 15 -cos (20) + 32 3 16 -cos(40). 1 32 -cos(60).
Show that sin4θ = 3/8 − 1/2cos(2θ) + 1/8 cos 4(θ) .
In Problems 34–50, establish each identity. 2 cot@cot(20) = cot² 0 - 1
Show that s in(4θ) = (cosθ)(4 sinθ− 8 sin3θ).
In Problems 34–50, establish each identity. 18 sin20cos² 0 = cos(40)
Show that sin2θ cos2θ= 1/8 − 1/8 cos(4θ) .
In Problems 43–48, use the figures to evaluate each function if f (x) = sin x, g(x) = cos x, and h(x) = tan x. x² + y² = 4 y a (x, 1) X x² + y² = 1 В (3₁) X
Show that sin4θ cos4θ = 3/128 − 1/32 cos(4θ) + 128 cos(8θ).
Find an expression for cos(3θ) as a third-degree polynomial in the variable cosθ.
In Problems 47–50, solve each equation on the interval 0 ≤ θ < 2π. sin (20) + sin(40) = 0
In Problems 49–74, establish each identity. COS cos(1/2 + 0). = - sin
In Problems 34–50, establish each identity. sin (30) cos sin cos (30) sin (20) 1
Find an expression for cos(4θ) as a fourth-degree polynomial in the variable cosθ.
In Problems 47–50, solve each equation on the interval 0 ≤ θ < 2π. cos (20)+cos (40) = 0
In Problems 49–74, establish each identity. ( 1/1 + 0) sin = cos
In Problems 34–50, establish each identity. sin (20) + sin(40) cos (20)+cos (40) tan (30)
In Problems 51–72, establish each identity. cos40 sin 40 = sin 40 = cos(20)
See Problem 51.(a) Write, as a product of sines and/or cosines, the sound emitted when the # key is touched.(b) Determine the maximum value of y.(c) Graph the sound emitted when the # key is
In Problems 47–50, solve each equation on the interval 0 ≤ θ < 2π. cos(40) cos(60) = 0
In Problems 34–50, establish each identity. cos(20) cos(40) cos(20) cos(40) tantan (30) = 0
In Problems 47–50, solve each equation on the interval 0 ≤ θ < 2π. sin (40) sin(60) = 0

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