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mathematics
precalculus

Questions and Answers of Precalculus

Solve equation on the interval 0 ≤ θ ≤ 2π.sin θ - cos θ = -√2
Solve equation on the interval 0 ≤ θ ≤ 2π.sin θ + cos θ = √2
Solve equation on the interval 0 ≤ θ ≤ 2π.√3 sin θ + cos θ = 1
Solve equation on the interval 0 ≤ θ ≤ 2π.sin θ – √3 cos θ = 1
Write trigonometric expression as an algebraic expression containing u and υ. Give the restrictions required on u and υ.sec(tan-1 u + cos-1 υ)
Write trigonometric expression as an algebraic expression containing u and υ. Give the restrictions required on u and υ.tan(sin-1 u - cos-1 υ)
Write trigonometric expression as an algebraic expression containing u and υ. Give the restrictions required on u and υ.cos(tan-1 u + tan-1 υ)
Write trigonometric expression as an algebraic expression containing u and υ. Give the restrictions required on u and υ.sin(tan-1 u - sin -1 υ)
Write trigonometric expression as an algebraic expression containing u and υ. Give the restrictions required on u and υ.sin(sin-1 u - cos-1 υ)
Write trigonometric expression as an algebraic expression containing u and υ. Give the restrictions required on u and υ.cos(cos-1 u + sin-1 υ)
Find the exact value of expression. -1 tanl cos cos + sin1
Find the exact value of expression. tan sin 5 + cos1
Find the exact value of expression. 3 TT tan 4 -1 cos
Find the exact value of expression. tan( sin+ 3 т 5 6.
Find the exact value of expression. 12 4 -1 cos tan 3 + cos 13 3.
Find the exact value of expression. 5 cos sin tan 13 4,
Find the exact value of expression. -1 cos tan sin 12
Find the exact value of expression. 4 cos tan 3 5 -1 + cos 13 3.
Find the exact value of expression. sin sin tan
Find the exact value of expression. 3 5 sin sin cos
Find the exact value of expression. V3 sin sin + cos1 2 2.
Find the exact value of expression. sin sin + cos 0 2
Establish identity.cos(θ + kπ) = (-1)k cos θ, k any integer
Establish identity.sin(θ + kπ) = (-1)k sin θ, k any integer
Establish identity.cos(α - β) cos(α + β) = cos2 α - sin2 β
Establish identity.sin(α – β) sin(α + β) = sin2 α - sin2 β
Establish identity. sec a sec B 1 + tan a tan B sec(a – B)
Establish identity. csc a csc B sec(a + B) cot a cot B – 1
Establish identity. cot a cot B + 1 cot B – cot a cot(a – B) =
Establish identity. cot a cot B – 1 cot B + cot a cot(a + B) %3D
Establish identity. cos(a + B) cos(a – 1 - tan a tan B B) 1 + tan a tan B
Establish identity. sin(a + B) sin(a - B) tan a + tan B - tan B tan a
Establish identity. |cos(a – B) в) cot a + tan B sin a cos B %3D
Establish identity. cos(a + B) = 1 – tan a tan B cos a cos B
Establish identity. sin(æ + B) tan a + tan B cos a cos B
Establish identity. sin(a + B) sin a cos B = 1 + cot a tan B
Establish identity.cos(α + β) + cos(α - β) = 2 cos α cos β
Establish identity.sin(α + β) + sin(α - β) = 2 sin α cos β
Establish identity. Зт cos sin 0
Establish identity. ++)- Зт sin cos 0 2.
Establish identity.tan(2π – θ) = -tan θ
Establish identity.tan(π – θ) = -tan θ
Establish identity.cos(π + θ) = -cos θ
Establish identity.sin(π + θ) = -sin θ
Establish identity.cos(π – θ) = -cos θ
Establish identity.sin(π – θ) = sin θ
Establish identity. TT cos 2 -sin 0 %3| ||
Establish identity. = cos e sin
Use the figures to evaluate function if f(x) = sin x, g(x) = cos x, and h(x) = tan x. h(α + β) х2 + у? 3 4 х2 + у2 3 1 (x, 1) 3.У
Use the figures to evaluate function if f(x) = sin x, g(x) = cos x, and h(x) = tan x. h(α - β) х2 + у? 3 4 х2 + у2 3 1 (x, 1) 3.У
Use the figures to evaluate function if f(x) = sin x, g(x) = cos x, and h(x) = tan x. f(α - β) х2 + у? 3 4 х2 + у2 3 1 (x, 1) 3.У
Use the figures to evaluate function if f(x) = sin x, g(x) = cos x, and h(x) = tan x. g(α - β) х2 + у? 3 4 х2 + у2 3 1 (x, 1) 3.У
Use the figures to evaluate function if f(x) = sin x, g(x) = cos x, and h(x) = tan x. g(α + β) х2 + у? 3 4 х2 + у2 3 1 (x, 1) 3.У
Use the figures to evaluate function if f(x) = sin x, g(x) = cos x, and h(x) = tan x. f(α + β) х2 + у? 3 4 х2 + у2 3 1 (x, 1) 3.У
If cos θ = 1/4, θ in quadrant IV, find the exact value of:(a) sin θ(b) sin(θ – π/6)(c) cos(θ – π/3)(d) tan(θ – π/4)
If sin θ = 1/3, θ in quadrant II, find the exact value of:(a) cos θ(b) sin(θ + π/6)(c) cos(θ - π/3)(d) tan(θ + π/4)
Find the exact value of the following under the given conditions:(a) sin(α + β)(b) cos(α + β)(c) sin(α - β)(d) tan(α - β) < a < 0; sin B 2 2' ,0 < B < cos a =
Find the exact value of the following under the given conditions:(a) sin(α + β)(b) cos(α + β)(c) sin(α - β)(d) tan(α - β) 5 5 Зт - < a < -; tan B = -V3, 13=-V3.
Find the exact value of the following under the given conditions:(a) sin(α + β)(b) cos(α + β)(c) sin(α - β)(d) tan(α - β) 5 tan a = 12' Зт π
Find the exact value of the following under the given conditions:(a) sin(α + β)(b) cos(α + β)(c) sin(α - β)(d) tan(α - β) TT ,0 < B < < a < T; cos B tan a = 3' 2 2
Find the exact value of the following under the given conditions:(a) sin(α + β)(b) cos(α + β)(c) sin(α - β)(d) tan(α - β) V5 4 , 0
Find the exact value of the following under the given conditions:(a) sin(α + β)(b) cos(α + β)(c) sin(α - β)(d) tan(α - β) 3 sin 0 < a
Find the exact value of expression. 5т cos TT п sin + cos 18 57 sin 18 18 18
Find the exact value of expression. 5п + sin cos 12 т sin 12 12 Cos 12
Find the exact value of expression. 5т sin 5т 7т sin 12 12 Ços cos 12 12
Find the exact value of expression. sin -cos Cos 12 12 sin Cos 12 12
Find the exact value of expression. tan 40° – tan 10° 1 + tan 40° tan 10°
Find the exact value of expression. tan 20° + tan 25° 1 - tan 20° tan 25°
Find the exact value of expression.cos 40° cos 10° + sin 40° sin 10°
Find the exact value of expression.cos 70° cos 20° - sin 70° sin 20°
Find the exact value of expression.sin 20° cos 80° - cos 20° sin 80°
Find the exact value of expression.sin 20° cos 10° + cos 20° sin 10°
Find the exact value of expression.cot (-5π/12)
Find the exact value of expression.sec (-π/12)
Find the exact value of expression.tan 19π/12
Find the exact value of expression.sin 17π/12
Find the exact value of expression.tan 195°
Find the exact value of expression.tan 15°
Find the exact value of expression.sin 105°
Find the exact value of expression.cos 165°
Find the exact value of expression.tan 7π/12
Find the exact value of expression.cos 7π/12
Find the exact value of expression.sin π/12
Find the exact value of expression.sin 5π/12
True or FalseIf f(x) = sin x and g(x) = cos x, then g(α + β) = g(α) g(β) - f(α)f(β)
True or Falsecos(π/2 – θ) = cos θ
True or Falsetan 75° = tan 30° + tan 45°
True or Falsesin(α + β) = sin α + sin β +2 sin α sin β
sin(α - β) = sin α cos β _______ cos α sin β
cos(α + β) = cos α cos β _______ sin α sin β
If sin α = -4/5, π < α < π3/2, then cos α = ______.
(a) sin π/4 ∙ cos π/3 = ______.(b) tan π/4 – sin π/6 = ______.
If sin θ = 4/5 and θ is in quadrant II, then cos θ = _______.
The distanced from the point (2, -3) to the point (5, 1) is _________.
Write down the three Pythagorean Identities.
Optical Measurement Optical methods of measurement often rely on the interference of two light waves. If two light waves, identical except for a phase lag, are mixed together, the resulting
Searchlights A searchlight at the grand opening of a new car dealership casts a spot of light on a wall located 75 meters from the searchlight. The acceleration P of the spot of light is found to be
Show that the functions f and g are identically equal. cos e 8(0) : 1 - sin e tan 0 + sec 0 f(0)
Show that the functions f and g are identically equal. 1 - sin 0 f(0) cos 0 8(0) = 0 1 + sin 0 cos e
Show that the functions f and g are identically equal.f(x) = cos x ∙ cot x g(x) = csc x - sin x

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