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mathematics
algebra and trigonometry graphs
Questions and Answers of
Algebra And Trigonometry Graphs
Factor and simplify, if possible. Check your result using a graphing calculator.sin4 x - cos4 x
Factor and simplify, if possible. Check your result using a graphing calculator.4 sin2 y + 8 sin y + 4
Factor and simplify, if possible. Check your result using a graphing calculator.2 cos2 x + cos x - 3
Prove each of the following identities.csc x - cos x cot x = sin x
Simplify and check using a graphing calculator 3 sin x cos²x cos²x + cos x sin x 2 sin²x - cos²x
Factor and simplify, if possible. Check your result using a graphing calculator.3 cot2 β + 6 cot β + 3
Prove each of the following identities.(sin x + cos x)2 = 1 + sin 2x
Simplify and check using a graphing calculator. sin²x cos x 2 cos x sin x
Prove each of the following identities. 1 + sin a 1 + csc a || tan a sec a
Simplify and check using a graphing calculator cot x CSC X 2 + 1 csc²x
Factor and simplify, if possible. Check your result using a graphing calculator.sin3 x + 27
Simplify and check using a graphing calculator 3 cos y sin y - 2 sin²y - cos²y
Find an equivalent expression for cos 4x in terms of function values of x.
Factor and simplify, if possible. Check your result using a graphing calculator.1 - 125 tan3 s
Simplify and check using a graphing calculator. 30 sin³x 6 cos²x cos x sin x
Simplify and check using a graphing calculator 2 4 sin x cos²x 16 sin²x cos x
Find an equivalent expression for sin4 θ in terms of function values of θ, 2θ, or 4θ, raised only to the first power.
Simplify and check using a graphing calculator. sin2x + 2sinx + 1 sin x + 1 -
Use the half-angle identities to evaluate exactly.cos 15°
In Exercises, assume that all radicands are nonnegative.Simplify: Vsin²x + 2 cos x sin x + cos²x .
Simplify and check using a graphing calculator. cos²a - 1 cos a + 1
In Exercises, assume that all radicands are nonnegative.Rationalize the denominator: 1 + sin x 1 - sin x
Use the half-angle identities to evaluate exactly.tan 67.5°
Use the half-angle identities to evaluate exactly. COS ㅠ 8
Simplify and check using a graphing calculator. csc (-x) cot (-x)
Simplify.(cos x - sin x)2
Simplify and check using a graphing calculator. 4 tant sec t + 2 sect 6 tant sect + 2 sect
Use the half-angle identities to evaluate exactly.sin 112.5°
Use the half-angle identities to evaluate exactly. sin 5 T 12
Simplify and check using a graphing calculator. sin+x sin²x cos x 2 cos²x
Use the half-angle identities to evaluate exactly.tan 75°
Write cos 41° cos 29° + sin 41° sin 29° as a trigonometric function of a single angle and then evaluate.
Simplify and check using a graphing calculator. 4 cos³x sin²x sin x 4 cos x, 2
Given that x = 3 tan θ, express √9 + x2 as a trigonometric function without radicals. Assume that 0 < θ < π/2.
Evaluate cos 3π/8 exactly.
Given that sin θ = 0.3416 and θ is in quadrant I, find each of the following using identities.sin 2θ
Evaluate sin 105° exactly.
Given that sin θ = 0.3416 and θ is in quadrant I, find each of the following using identities. COS 0 2
Given that sin θ = 0.3416 and θ is in quadrant I, find each of the following using identities. sin 0 2
Simplify and check using a graphing calculator. sin²6 sin² - cos²6 &
Simplify and check using a graphing calculator. tan² y sec y ·1· 3 tany sec y
Solve, finding all solutions in [0, 2π).4 cos2 x = 3
Simplify: cos 27° cos 16° + sin 27° sin 16°.
Simplify and check using a graphing calculator. 1 sin's cos² s - COS S 2 - sin s
Find the exact value of sin 2θ and the quadrant in which 2θ lies if cos θ = -4/5 and θ is in quadrant II.
Solve, finding all solutions in [0, 2π).2 sin2 x = √2 sin x
Find cos 165° exactly.
Simplify and check using a graphing calculator. 2 x)² sin x COS X I 1 2 cos²x
Given that sin θ = 0.3416 and θ is in quadrant I, find each of the following using identities.sin 4θ
Simplify and check using a graphing calculator. 9 cos² a 25 2 cos a - 2 cos a 1 6 cos a - 10 -
Simplify and check using a graphing calculator. sin² 09 10 cos 0 + 5 2 cos 0 + 1 3 sin 0 + 9
Solve, finding all solutions in [0, 2π).√3 cos x + sin x = 1
Find cos θ, given that cos 20 5 6' Зп 2
Given that tan α = √3 and sin β = √2/2 and that α and β are between 0 and π/2, evaluate tan (α - β) exactly.
Complete the cofunction identity. cos ( x + TT 2 =
Assume that sin θ = 0.5812 and cos ϕ = 0.2341 and that both θ and ϕ are first-quadrant angles. Evaluate cos (θ + ϕ).
Complete the cofunction identity. COS TT 2 -x) =
Complete the cofunction identity. sin x TT 2 =
Simplify and check using a graphing calculator. Assume that all radicands are nonnegative. sin²x cos x Vcos x .
Simplify and check using a graphing calculator. Assume that all radicands are nonnegative. Vcos² cos²x sinx. Vsin x
Explain why tan (x + 450°) cannot be simplified using the tangent sum formula, but can be simplified using the sine and cosine sum formulas.
Simplify and check using a graphing calculator. Assume that all radicands are nonnegative. Vco cos a sin² a Vcos³ a COS
Derive the product-to-sum identities (3) and (4) using the sine sum and difference identities.
Discuss and compare the graphs of y = sin x, y = sin 2x, and y = sin 1x>22.
Derive the sum-to-product identities (5)–(8) using the product-to-sum identities (1)–(4).
Given that cos α = -3/5 and that the terminal side is in quadrant III:a) Find the other function values for α.b) Find the six function values for π/2 - α. c) Find the six function values for
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.sin 3θ - sin 5θ
Use the product-to-sum identities and the sum-to-product identities to prove each of the following. tan 0 + 0 2 -(sin - sin ) = tan 0 – ф 2 -(sin 0 + sin )
Simplify and check using a graphing calculator.2 sin x cos3 x + 2 sin3 x cos x
State the ranges of the inverse sine, inverse cosine, and inverse tangent functions.
Find an equivalent expression for CSC X EN
Simplify and check using a graphing calculator. Assume that all radicands are nonnegative. tan²x - 2 tan x sin x + sin²x
Simplify and check using a graphing calculator. Assume that all radicands are nonnegative. (1 - Vsin y) (Vsin y + 1)
Find all errors in the following:2 sin2 2x + cos 4x= 2(2 sin x cos x)2 + 2 cos 2x= 8 sin2 x cos2 x + 2(cos2 x + sin2 x)= 8 sin2 x cos2 x + 2.
An airplane is flying at an altitude of 2000 ft toward Logan International Airport, in Boston, Massachusetts. The straight-line distance from the airplane to the airport is d feet. Express θ, the
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.sin 7x - sin 4x
Simplify and check using a graphing calculator. Assume that all radicands are nonnegative. Vcos (√2 cos 0 + V sin 0 cos 0)
Find tan 2θ, cos 2θ, and sin 2θ and the quadrant in which 2θ lies, where cos θ = -4/5 and θ is in quadrant III.
A guy wire is attached to the top of a 50-ft pole and stretched to a point that is d feet from the bottom of the pole. Express β, the angle of inclination, as a function of d. 50 ft K g -d-
Given that sin β = 0.2183 and β is in quadrant I, find sin 2β,and cos 4β. COS В
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.sin 8θ + sin 5θ
Simplify and check using a graphing calculator X 1 - 2 sin². 2 2
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.cos θ - cos 7θ
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.sin 7u sin 5u
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.2 sin 7θ cos 3θ
Simplify and check using a graphing calculator(sin x + cos x)2 - sin 2x
Complete the identity.1 - cos2 x =
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.7 cos θ sin 7θ
Complete the identity.sec2 x - tan2 x =
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.cos 55° sin 25°
Complete the identity.1 + cot2 x =
Simplify and check using a graphing calculator. 2 cot x cot²x - 1
Use the product-to-sum identities and the sum-to-product identities to find identities for each of the following.cos 2t sin t
Complete the identity.sin2 x - 1 =
Complete the identity.csc2 x - cot2 x
Use the product-to-sum identities and the sum-to-product identities to prove each of the following. tan x + y 2 sin x + sin y cos x + cos y
Use the product-to-sum identities and the sum-to-product identities to prove each of the following.sin 4θ + sin 6θ = cot θ (cos 4θ - cos 6θ)
Complete the identity.1 + tan2 x =
Use the product-to-sum identities and the sum-to-product identities to prove each of the following.tan 2x (cos x + cos 3x) = sin x + sin 3x
Complete the identity.1 - sin2 x
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