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mathematics
algebra and trigonometry graphs

Questions and Answers of Algebra And Trigonometry Graphs

Use the product-to-sum identities and the sum-to-product identities to prove each of the following. cot x + y 2 = sin y - sin x COS X cos y -
Use the product-to-sum identities and the sum-to-product identities to prove each of the following.cot 4x (sin x + sin 4x + sin 7x) = cos x + cos 4x + cos 7x
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.3 cos 2θ sin θ
Complete the identity.sec2 x - 1
Solve using a calculator, finding all solutions in [0, 2π).x2 + 2 = sin x
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.sin θ - sin 4θ
Solve using a calculator, finding all solutions in [0, 2π).2 cos2 x = x + 1
Solve using a calculator, finding all solutions in [0, 2π). sin x = tan X 2
Solve using a calculator, finding all solutions in [0, 2π).x cos x - 2 = 0
Use the product-to-sum identities and the sum-to-product identities to prove each of the following. tan 0 + 6 2 tan - 0 2 = cos cos cos 0 + cos -
Sales of fishing boats fluctuate in cycles. The following cosine function can be used to estimate the total amount of sales of fishing boats, y, in thousands of dollars, in month x, for a business: y
Solve using a calculator, finding all solutions in [0, 2π).cos x - 2 = x2 - 3x
Use the sum and difference identities to evaluate exactly. Then check using a graphing calculator. sin TT 12
In Exercises, use a graphing calculator to determine which expression (A)–(F) on the right can be used to complete the identity. Then try to prove that identity algebraically.A.B. cos xC. tan x +
Find each of the following exactly in both radians and degrees. − sin 1 I 2,
Find each of the following exactly in both radians and degrees. -1 COS √3 2
Use the product-to-sum identities and the sum-to-product identities to prove each of the following.sin 2θ + sin 4θ + sin 6θ = 4 cos θ cos 2θ sin 3θ
Given that cos 51° ≈ 0.6293, find the six function values for 141°.
In Exercises, use a graphing calculator to determine which expression (A)–(F) on the right can be used to complete the identity. Then try to prove that identity algebraically.A.B. cos xC. tan x +
In Exercises, use a graphing calculator to determine which expression (A)–(F) on the right can be used to complete the identity. Then try to prove that identity algebraically.A.B. cos xC. tan x +
Simplify. Check your results using a graphing calculator. cot x sin (x-7) 2 cos (x) + cotx sin
The data in the following table give the average high temperature in Chicago for certain months.a) Using the SINE REGRESSION feature on a graphing calculator, fit a sine function of the form y = A
Find sin 15° first using a difference identity and then using a half-angle identity. Then compare the results.
Sales of certain products fluctuate in cycles. The following sine function can be used to estimate the total amount of sales of skis, y, in thousands of dollars, in month x, for a business in a
Use the sum and difference identities to evaluate exactly. Then check using a graphing calculator.cos 75°
Use the sum and difference identities to evaluate exactly. Then check using a graphing calculator. tan 5TT 12
Simplify. Check your results using a graphing calculator. sin (7. - x) | sec x - cos x 2
The data in the following table give the number of daylight hours for certain days in Kajaani, Finland.a) Using the SINE REGRESSION feature on a graphing calculator, model these data with an equation
Use the sum and difference identities to evaluate exactly. Then check using a graphing calculator.tan 105°
Find each of the following exactly in both radians and degrees.tan-1 1
In Exercises, use a graphing calculator to determine which expression (A)–(F) on the right can be used to complete the identity. Then try to prove that identity algebraically.A.B. cos xC. tan x +
Solve, finding all solutions. Express the solutions in both radians and degrees. cos x = X √2 2
Assuming that sin θ = 0.6249 and cos ϕ = 0.1102 and that both θ and ϕ are first-quadrant angles, evaluate each of the following.tan (θ + ϕ)
Use the sum and difference identities to evaluate exactly. Then check using a graphing calculator.cos 15°
Simplify. Check your results using a graphing calculator. cos² y sin (y + sin²y sin 2 TT 2 y
Simplify. Check your results using a graphing calculator. COS X - sin - ㅠ 2 - X sin x COS X COS (π - x) tan x
In Exercises, use a graphing calculator to determine which expression (A)–(F) on the right can be used to complete the identity. Then try to prove that identity algebraically.A.B. cos xC. tan x +
Find each of the following exactly in both radians and degrees.sin-1 0
Use the sum and difference identities to evaluate exactly. Then check using a graphing calculator. sin TT 1 п 12
In Exercises, use a graphing calculator to determine which expression (A)–(F) on the right can be used to complete the identity. Then try to prove that identity algebraically.A.B. cos xC. tan x +
Find sin θ, cos θ, and tan θ under the given conditions. tan Ө 2 || 5 3' П
Use a calculator to find each of the following in radians, rounded to four decimal places, and in degrees, rounded to the nearest tenth of a degree.cos-1 ( -0.2194)
Find sin θ, cos θ, and tan θ under the given conditions. cos 20 7 3п 12' 2 < 20 < 2п
Use a calculator to find each of the following in radians, rounded to four decimal places, and in degrees, rounded to the nearest tenth of a degree.cot-1 2.381
Solve in [0, 2π). | cos x 1 1. 2
Solve in [0, 2π). \sin x V3 2
First write each of the following as a trigonometric function of a single angle. Then evaluate.sin 37° cos 22° + cos 37° sin 22°
For each function:a) Graph the function.b) Determine whether the function is one-to-one.c) If the function is one-to-one, find an equation for its inverse.d) Graph the inverse of the function.f(x) =
First write each of the following as a trigonometric function of a single angle. Then evaluate.cos 83° cos 53° + sin 83° sin 53°
For each function:a) Graph the function.b) Determine whether the function is one-to-one.c) If the function is one-to-one, find an equation for its inverse.d) Graph the inverse of the function.f(x) =
Solve in [0, 2π). tan x = #3
First write each of the following as a trigonometric function of a single angle. Then evaluate.cos 19° cos 5° - sin 19° sin 5°
First write each of the following as a trigonometric function of a single angle. Then evaluate. tan 20° + tan 32° 1 - tan 20° tan 32°
For each function:a) Graph the function.b) Determine whether the function is one-to-one.c) If the function is one-to-one, find an equation for its inverse.d) Graph the inverse of the function.f(x) =
First write each of the following as a trigonometric function of a single angle. Then evaluate.sin 40° cos 15° - cos 40° sin 15°
First write each of the following as a trigonometric function of a single angle. Then evaluate. tan 35° - tan 12° 1+tan 35° tan 12°
For each function:a) Graph the function.b) Determine whether the function is one-to-one.c) If the function is one-to-one, find an equation for its inverse.d) Graph the inverse of the function.f(x) =
Solve.2x2 = 5x
Solve in [0, 2π).esin x = 1
Solve.3x2 + 5x - 10 = 18
Solve in [0, 2π).ln (cos x) = 0
Derive the formula for the tangent of a sum.
Solve.x4 + 5x2 - 36 = 0
Solve, finding all solutions. Express the solutions in both radians and degrees. tan x = √3
Solve in [0, 2π).eln (sin x) = 1
Derive the formula for the tangent of a difference.
Solve.x2 - 10x + 1 = 0
Solve, finding all solutions in [0, 2π).4 sin2 x = 1 ул 4 - 3 2 М y=1 TT 1 2п х y = 4 sin2 x
Solve in [0, 2π).sin (ln x) = -1
Assuming that sin u = 3/5 and sin v = 4/5 and that u and v are between 0 and π/2, evaluate each of the following exactly.cos (u + v)
Solve.√x - 2 = 5
Solve, finding all solutions in [0, 2π).sin 2x sin x - cos x = 0 YA 2 1 -2 y = sin 2x sin x - cos x TT y = 0 PTT X
Solve in [0, 2π).12 sin x - 7√sin x + 1 = 0
Assuming that sin u = 3/5 and sin v = 4/5 and that u and v are between 0 and π/2, evaluate each of the following exactly.tan (u - v)
The temperature T, in degrees Fahrenheit, of a patient t days into a 12-day illness is given byFind the times t during the illness at which the patient’s temperature was 103°. T(t) = 101.6° + 3°
Solve.x = √x + 7 + 5
A satellite circles the earth in such a manner that it is y miles from the equator (north or south, height from the surface not considered) t minutes after its launch, whereAt what times t on the
Assuming that sin u = 3/5 and sin v = 4/5 and that u and v are between 0 and π/2, evaluate each of the following exactly.sin (u - v)
Solve, finding all solutions in [0, 2π).2 cos2 x + 3 cos x = -1
Solve, finding all solutions in [0, 2π).sin2 x - 7 sin x = 0
The following equation occurs in the study of mechanics:It can happen that I1 = I2. Assuming that this happens, simplify the equation. sin 0 = I cos o (1₁ cos )² + (1₂sin 6)² V
Assuming that sin u = 3/5 and sin v = 4/5 and that u and v are between 0 and π/2, evaluate each of the following exactly.cos (u - v)
Solve, finding all solutions in [0, 2π).csc2 x - 2 cot2 x = 0
In the theory of alternating current, the following equation occurs:Show that this equation is equivalent to R= 1 wC (tantan)
Assuming that cos α = - 3/7 with a between π/2 and p and that cos β = 8/9 with b between 3π/2 and 2π, evaluate each of the following exactly.cos (α + β)
Solve, finding all solutions in [0, 2π).sin 4x + 2 sin 2x = 0
Assuming that cos α = - 3/7 with a between π/2 and p and that cos β = 8/9 with b between 3π/2 and 2π, evaluate each of the following exactly.sin (α - β)
In electrical theory, the following equations occur:Assuming that these equations hold, show that and E₁ = √2E₁ E₂ = √2E₁ s (0 + =/ ) P COS COS 0 - F). P
Solve, finding all solutions in [0, 2π).2 cos x + 2 sin x = √2
Simplify:A. -π/6 B. 7π/6C. -1/2 D. 11π/6 -1 sin sin 7πT 6
Solve, finding all solutions in [0, 2π).6 tan2 x = 5 tan x + sec2 x
Assuming that sin θ = 0.6249 and cos ϕ = 0.1102 and that both θ and ϕ are first-quadrant angles, evaluate each of the following.sin (θ - ϕ)
Solve using a graphing calculator, finding all solutions in [0, 2π).x cos x = 1
Assuming that sin θ = 0.6249 and cos ϕ = 0.1102 and that both θ and ϕ are first-quadrant angles, evaluate each of the following.cos (θ - ϕ)
Solve using a graphing calculator, finding all solutions in [0, 2π).2 sin2 x = x + 1
Assuming that sin θ = 0.6249 and cos ϕ = 0.1102 and that both θ and ϕ are first-quadrant angles, evaluate each of the following.cos (θ + ϕ)
Which of the following is the domain of the function cos-1 x ?A. (0, π) B. [ -1, 1]C. [ -π/2, π/2] D. ( -∞, ∞)
Simplify.sin (α + β) + sin (α - β)
Find sin θ, cos θ, and tan θ under the given conditions: sin 20 = I 5' TT E|N < 20 < TT.
Simplify.cos (α + β) - cos (α - β)

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