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study help
mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, rewrite the expression with an exponent no higher than 1.cos2 (5x)
For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first.f(θ) = cos(2θ), g(θ) = cos2 θ − sin2 θ
For the following exercises, solve with the methods shown in this section exactly on the interval [0, 2π).cos(2t) = sin t
For the following exercises, rewrite the sum as a product of two functions or the product as a sum of two functions. Give your answer in terms of sines and cosines. Then evaluate the final answer numerically, rounded to four decimal places.cos(58°) + cos(12°)
For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. f(0) =tan(20), g(0) = tan 0 1 + tan²0
For the following exercises, construct an equation that models the described behavior.A spring attached to the ceiling is pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models
For the following exercises, rewrite the expression with an exponent no higher than 1.cos2 (6x)
For the following exercises, determine whether the identity is true or false. If false, find an appropriate equivalent expression. cos² 1 - sin² 0 tan²0 = sin² 0
For the following exercises, solve with the methods shown in this section exactly on the interval [0, 2π).cos(6x) − cos(3x) = 0
For the following exercises, rewrite the sum as a product of two functions or the product as a sum of two functions. Give your answer in terms of sines and cosines. Then evaluate the final answer numerically, rounded to four decimal places.sin(2°) − sin(3°)
For the following exercises, construct an equation that models the described behavior.A spring attached to the ceiling is pulled 19 cm down from equilibrium and released. After 4 seconds, the amplitude has decreased to 14 cm. The spring oscillates 13 times each second. Find a function that models
For the following exercises, rewrite the expression with an exponent no higher than 1.sin4 (8x)
For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. f(x) = sin(3x)sin x, g(x) = sin²(2x) cos²x - cos²(2x)sin² x
For the following exercises, solve exactly on the interval [0, 2π).Use the quadratic formula if the equations do not factor. tan2 x − √3 tan x = 0
For the following exercises, rewrite the sum as a product of two functions or the product as a sum of two functions. Give your answer in terms of sines and cosines. Then evaluate the final answer numerically, rounded to four decimal places.cos(44°) − cos(22°)
For the following exercises, determine whether the identity is true or false. If false, find an appropriate equivalent expression.3 sin2 θ + 4 cos2 θ = 3 + cos2 θ
For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. f(x) =tan(-x), g(x) tan x - tan(2x) 1 tan xtan(2x) -
For the following exercises, create a function modeling the described behavior. Then, calculate the desired result using a calculator.A certain lake currently has an average trout population of 20,000. The population naturally oscillates above and below average by 2,000 every year. This year, the
For the following exercises, rewrite the expression with an exponent no higher than 1.sin4 (3x)
For the following exercises, solve exactly on the interval [0, 2π).Use the quadratic formula if the equations do not factor.sin2 x + sin x−2 = 0
For the following exercises, determine whether the identity is true or false. If false, find an appropriate equivalent expression. sec 0 + tan 0 cot 0 + cos 0 Ꮎ = sec²0
For the following exercises, rewrite the sum as a product of two functions or the product as a sum of two functions. Give your answer in terms of sines and cosines. Then evaluate the final answer numerically, rounded to four decimal places.cos(176°)sin(9°)
For the following exercises, create a function modeling the described behavior. Then, calculate the desired result using a calculator.Whitefish populations are currently at 500 in a lake. The population naturally oscillates above and below by 25 each year. If humans overfish, taking 4% of the
For the following exercises, rewrite the expression with an exponent no higher than 1.cos2 x sin4 x
For the following exercises, find the exact value algebraically, and then confirm the answer with a calculator to the fourth decimal point.sin(75°)
For the following exercises, solve exactly on the interval [0, 2π).Use the quadratic formula if the equations do not factor.sin2 x − 2sin x−4 = 0
For the following exercises, construct an equation that models the described behavior. A deer population oscillates 19 above and below average during the year, reaching the lowest value in January. The average population starts at 800 deer and increases by 160 each year.Find a function that
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. 0 1 x y-2 23 4 4 10 4 -2 5 6 4 10
For the following exercises, find all solutions exactly on the interval 0 ≤ θ < 2π.tan x = 1
For the following exercises, find the exact value,tan (19π/12)
For the following exercises, find all solutions exactly on the interval 0 ≤ θ < 2π.cot x + 1 = 0
For the following exercises, rewrite in terms of sin x and cos x.sin (x + 11π/6)
For the following exercises, find all solutions exactly on the interval 0 ≤ θ < 2π.4sin2 x − 2 = 0
For the following exercises, rewrite the sum or difference as a product.cos(6t) + cos(4t)
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. 1 - sin x 1 + sin x 1 + sin x sin x 1 ; sec x and tan x
For the following exercises, evaluate the product using a sum or difference of two functions. Leave in terms of sine and cosine.2sin(100°)sin(20°)
For the following exercises, evaluate the product using a sum or difference of two functions. Leave in terms of sine and cosine.2cos(56°)cos(47°)
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.tan (π/4 − x)
For the following exercises, find the amplitude, period, and frequency of the given function.The displacement h(t) in centimeters of a mass suspended by a spring is modeled by the function h(t) = 8sin(6πt),where t is measured in seconds. Find the amplitude, period, and frequency of this
For the following exercises, find all exact solutions on [0, 2π).tan2 (x) = −1 + 2tan(−x)
For the following exercises, verify the identity.cos x(tan x − sec(−x)) = sin x − 1
For the following exercises, rewrite the sum as a product of two functions. Leave in terms of sine and cosine.cos(100°) + cos(200°)
For the following exercises, simplify each expression. Do not evaluate.1 − 2 sin2 (17°)
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.cos (7π/6 + x)
For the following exercises, find the amplitude, period, and frequency of the given function.The displacement h(t) in centimeters of a mass suspended by a spring is modeled by the function h(t) = 11sin(12πt), where t is measured in seconds. Find the amplitude, period, and frequency of this
For the following exercises, find all exact solutions on [0, 2π).8sin2 (x) + 6sin(x) + 1 = 0
For the following exercises, verify the identity. 1 + sin² x cos²x 1 cos² x + sin² x cos² x = 1 + 2 tan² x
For the following exercises, rewrite the sum as a product of two functions. Leave in terms of sine and cosine.sin(−1°) + sin(−2°)
For the following exercises, simplify each expression. Do not evaluate.cos2 (9x) − sin2 (9x)
For the following exercises, prove the identity. cos(a + b) cos(a - b) 1 tan a tan b 1 + tan a tan b
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.sin (π/4 + x)
For the following exercises, find all exact solutions on [0, 2π).tan5 (x) = tan(x)
For the following exercises, verify the identity.(sin x + cos x)2 = 1 + 2 sin x cos x
For the following exercises, simplify each expression. Do not evaluate.4 sin(8x) cos(8x)
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.cos (5π/4 + x)
For the following exercises, construct an equation that models the described behavior.he displacement h(t), in centimeters, of a mass suspended by a spring is modeled by the function h(t) = −5 cos(60πt), where t is measured in seconds. Find the amplitude, period, and frequency of this
For the following exercises, solve with the methods shown in this section exactly on the interval [0, 2π).sin(3x)cos(6x) − cos(3x)sin(6x) = −0.9
For the following exercises, prove the identity.4sin(3x)cos(4x) = 2 sin(7x) − 2 sinx
For the following exercises, verify the identity.cos2 x − tan2 x = 2 − sin2 x − sec2 x
For the following exercises, simplify each expression. Do not evaluate. 6 sin(5x) cos(5x)
For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first.f(x) = sin(4x) − sin(3x)cos x, g(x) = sin x cos(3x)
For the following exercises, prove or disprove the identity. 1 1 + cos x 1 1 - cos(-x) -2 cot xcsc x
For the following exercises, solve with the methods shown in this section exactly on the interval [0, 2π).sin(6x)cos(11x) − cos(6x)sin(11x) = −0.1
For the following exercises, prove the identity.6cos(8x)sin(2x)/sin(−6x) = −3 sin(10x)csc(6x) + 3
For the following exercises, prove the identity given.(sin t − cos t)2 = 1 − sin(2t)
For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first.f(x) = cos(4x) + sin xsin(3x), g(x) = −cos xcos(3x)
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. 0 у 5 2 1 4 -3 6 8 10 12 1 5 1-3
For the following exercises, solve exactly on [0, 2π).2sin(πθ) = 1
For the following exercises, evaluate the product using a sum or difference of two functions. Evaluate exactly.sin(−45°)sin(−15°)
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.(sec x + csc x)(sin x + cos x) − 2 − cot x; tan x
For the following exercises, find the exact values of a) sin (x/2), b) cos (x/2), and c) tan (x/2) without solving for x, when 0 ≤ x ≤ 360°.If sin x = −12/13, and x is in quadrant III.
For the following exercises, solve exactly on [0, 2π). 2cos(0) = √3 5
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.A Ferris wheel is 20 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o’clock position on the Ferris wheel is
For the following exercises, find the requested information.Given that sin a = 4/5, and cos b = 1/3, with a and b both in the interval [0,π/2), find sin(a − b) and cos(a + b).
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. 1 csc x sin x ; sec x and tan x
For the following exercises, evaluate the product using a sum or difference of two functions. Leave in terms of sine and cosine.cos(23°)sin(17°)
For the following exercises, find the exact values of a) sin (x/2), b) cos (x/2), and c) tan (x/2) without solving for x, when 0 ≤ x ≤ 360°.If csc x = 7, and x is in quadrant II.
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.A Ferris wheel is 45 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is
For the following exercises, find all exact solutions on [0, 2π).sec(x)sin(x) − 2sin(x) = 0
For the following exercises, find the exact values of a) sin (x/2), b) cos (x/2), and c) tan (x/2) without solving for x, when 0 ≤ x ≤ 360°.If sec x = −4, and x is in quadrant II.
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.The sea ice area around the North Pole fluctuates between about 6 million square kilometers on September 1 to 14 million square kilometers on March 1.
For the following exercises, find all exact solutions on [0, 2π).tan(x) − 2sin(x)tan(x) = 0
For the following exercises, evaluate the product using a sum or difference of two functions. Leave in terms of sine and cosine.2sin(−100°)sin(−20°)
For the following exercises, use Figure 5 to find the requested half and double angles.Find sin(2θ), cos(2θ), and tan(2θ). 5 α 12 Figure 5 0
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.tan x; sec x
For the following exercises, find the requested information. tan (sin '(1) - cos ¹()) 2
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.The sea ice area around the South Pole fluctuates between about 18 million square kilometers in September to 3 million square kilometers in March.
For the following exercises, find all exact solutions on [0, 2π).2cos2 t + cos(t) = 1
For the following exercises, evaluate the product using a sum or difference of two functions. Leave in terms of sine and cosine.sin(213°)cos(8°)
For the following exercises, use Figure 5 to find the requested half and double angles.Find sin(2α), cos(2α), and tan(2α). 5 α 12 Figure 5 Ꮎ
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.sec x; cot x
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.During a 90-day monsoon season, daily rainfall can be modeled by sinusoidal functions. If the rainfall fluctuates between a low of 2 inches on day 10 and
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.cos (π/2 − x)
For the following exercises, find all exact solutions on [0, 2π).2tan2 (t) = 3sec(t)
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.sec x; sin x
For the following exercises, use Figure 5 to find the requested half and double angles.Find sin (θ/2) , cos (θ/2) , and tan (θ/2). 5 α 12 Figure 5 0
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.During a 90-day monsoon season, daily rainfall can be modeled by sinusoidal functions. A low of 4 inches of rainfall was recorded on day 30, and overall
For the following exercises, rewrite the sum as a product of two functions. Leave in terms of sine and cosine.sin(76°) + sin(14°)
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.sin(π − x)
For the following exercises, find all exact solutions on [0, 2π).2sin(x)cos(x) − sin(x) + 2cos(x) − 1 = 0
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