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study help
mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.cot x; sin x
For the following exercises, use Figure 5 to find the requested half and double angles.Find sin (α/2) , cos (α/2) , and tan (α/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.In a certain region, monthly precipitation peaks at 8 inches on June 1 and falls to a low of 1 inch on December 1. Identify the periods when the region is
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.tan (π/3 + x)
For the following exercises, find all exact solutions on [0, 2π).cos2 θ = 1/2
For the following exercises, rewrite the sum as a product of two functions. Leave in terms of sine and cosine.cos(58°) − cos(12°)
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.cot x; csc x
For the following exercises, simplify each expression. Do not evaluate.cos2 (28°) − sin2 (28°)
For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical.sin (π/3 + x)
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.In a certain region, monthly precipitation peaks at 24 inches in September and falls to a low of 4 inches in March. Identify the periods when the region
For the following exercises, find all exact solutions on [0, 2π).sec2 x = 1
For the following exercises, rewrite the sum as a product of two functions. Leave in terms of sine and cosine.sin(101°) − sin(32°)
For the following exercises, verify the identity.cos x − cos3 x = cos x sin2 x
For the following exercises, simplify the given expression. (²/2x). 3 2 tan 1 + tan tan (2x) 7 x)tan ( (3x) 5 -
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. 1 1 - cos x COS X 1 + cos x ; CSC X
For the following exercises, simplify each expression. Do not evaluate.2 cos2 (37°) − 1
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the temperature varies between 64°F and 86°F during the
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the temperature varies between 47°F and 63°F during the
For the following exercises, solve exactly on [0, 2π).cos(2θ) = −√3/2
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 tan x = −4/3, and x is in quadrant IV.
For the following exercises, find the requested information. Given that sin a = 2/3 and cos b = −1/4, with a and b both in the interval [π/2 , π), find sin(a + b) and cos(a − b).
For the following exercises, evaluate the product using a sum or difference of two functions. Evaluate exactly.sin(195°)cos(15°)
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. 1 sin x cos x - cot x; cot x
For the following exercises, find the exact value using half-angle formulas.tan (−3π/8)
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. secx + csc x; sin x 1 + tan x
For the following exercises, evaluate the product using a sum or difference of two functions. Evaluate exactly.sin(−345°)sin(−15°)
For the following exercises, solve exactly on [0, 2π).2cos(3θ) = −√2
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. COS X 1 + sin x + tan x; cos x
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of 84°F occurs at 6PM and the average
For the following exercises, simplify the given expression.sin(2x) cos(5x) − sin(5x) cos(2x)
For the following exercises, solve exactly on [0, 2π).2sin(3θ) = 1
For the following exercises, evaluate the product using a sum or difference of two functions. Evaluate exactly.cos(45°)sin(15°)
For the following exercises, find the exact value using half-angle formulas.tan (5π/12)
For the following exercises, solve exactly on [0, 2π).2sin(2θ) = √3
For the following exercises, find the exact value using half-angle formulas.tan (−3π/12)
For the following exercises, evaluate the product using a sum or difference of two functions. Evaluate exactly.cos(45°)cos(15°)
For the following exercises, construct a sinusoidal function with the provided information, and then solve the equation for the requested values.Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of 105°F occurs at 5PM and the
For the following exercises, simplify the given expression.tan (π/2 − x)
For the following exercise, construct a function modeling behavior and use a calculator to find desired results.A city’s average yearly rainfall is currently 20 inches and varies seasonally by 5 inches. Due to unforeseen circumstances, rainfall appears to be decreasing by 15% each year. How many
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. tan x + cotx; cos x CSC X
For the following exercises, simplify the given expression.cot (π/2 − x)
For the following exercises, find the exact value using half-angle formulas.cos (7π/8)
For the following exercises, rewrite the sum or difference as a product.sin h − sin(3h)
For the following exercises, graph the given function, and then find a possible physical process that the equation could model. XT f(x) = 10 — sin (X7 ) - 24tan( on the interval [0, 80] 6 240
For the following exercises, solve exactly on [0, 2π).2sin θ = −√3
For the following exercises, simplify the given expression.sec (π/2−θ)
For the following exercises, use the fundamental identities to fully simplify the expression. 1 - cos² x tan² x + 2 sin² x
For the following exercises, find the exact value using half-angle formulas.sin (11π/12)
For the following exercises, rewrite the sum or difference as a product.cos(3x) + cos(9x)
For the following exercises, graph the given function, and then find a possible physical process that the equation could model. f(x)=-18cos( (17) - -5sin (7) + - 12 12 + 100 on the interval [0, 24]
For the following exercises, solve exactly on [0, 2π).2sin θ = −1
For the following exercises, simplify the given expression.csc (π/2 − t)
For the following exercises, use the fundamental identities to fully simplify the expression. tan x csc² x tan x + 1 + tan x 1+cot x 1 cos² x
For the following exercises, find the exact value using half-angle formulas.cos (−11π/12)
For the following exercises, rewrite the sum or difference as a product.sin(3x) − sin(−3x)
For the following exercises, graph the given function, and then find a possible physical process that the equation could model. f(x) = -30cos ²-)- ХЛ 6 ХП ps²( X ) + 80 [0, 12] 6 20cos²
For the following exercises, solve exactly on [0, 2π).2cos θ = −1
For the following exercises, rewrite in terms of sin x and cos x.cos (x + 2π/3)
For the following exercises, use the fundamental identities to fully simplify the expression. 1 + tan²0 csc² 0 + sin² 0 + 1 sec² 0
For the following exercises, find the exact value using half-angle formulas. sin (π/8)
For the following exercises, rewrite the sum or difference as a product.cos(7x) + cos(−7x)
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. X y -1 √3-2 0 0 1 2-√3 2 V3 3 3 1 4 V3 5 2+√3
For the following exercises, solve exactly on [0, 2π).2cos θ = √2
For the following exercises, rewrite in terms of sin x and cos x.cos (x −5π/6)
We can determine the half-angle formula for tan (x/2) = ± √1 − cos x/√1 + cos x by dividing the formula for sin (x/2) by cos (x/2).Explain how to determine two formulas for tan (x/2) that do not involve any square roots.
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. X 03 6 9 12 15 y -4 -1 2-1-4-1 ४४ 18 2
For the following exercises, find the exact value. cos (π/12)
For the following exercises, rewrite the product as a sum or difference.20cos(36t)cos(6t)
For the following exercises, use the fundamental identities to fully simplify the expression.sin(−x)cos(−x)csc(−x)
For the following exercises, find the exact values of a) sin(2x), b) cos(2x), and c) tan(2x) without solving for x.If cos x = 2/3 , and x is in quadrant I.
For the following exercises, find the exact value.sin (5π/12)
For the following exercises, find all solutions exactly on the interval 0 ≤ θ < 2π.2cos θ = −√2
For the following exercises, rewrite the product as a sum or difference.2sin(5x)cos(3x)
For the following exercises, use the fundamental identities to fully simplify the expression.tan x sin x + sec x cos2 x
For the following exercises, find the exact values of a) sin(2x), b) cos(2x), and c) tan(2x) without solving for x.If cos x = −1/2 , and x is in quadrant III.
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. X y 0 2 П 4 7 П 2 2 Зл 4 -3 π 2 5п 4 7 Зл 2 2
For the following exercises, find the exact value,sin (11π/12)
For the following exercises, find all solutions exactly on the interval 0 ≤ θ < 2π.tan θ = −1
For the following exercises, rewrite the product as a sum or difference.10cos(5x)sin(10x)
For the following exercises, use the fundamental identities to fully simplify the expression.csc x + cos x cot(−x)
For the following exercises, find the exact values of a) sin(2x), b) cos(2x), and c) tan(2x) without solving for x.If tan x = −8, and x is in quadrant IV.
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. X 0 1 2 34 5 y 1 -3 -7 -3 1-3 6 -3-7
For the following exercises, find the exact value,tan (−π/ 12)
For the following exercises, rewrite the product as a sum or difference.sin(−x)sin(5x)
For the following exercises, use the fundamental identities to fully simplify the expression.cot t + tan t/sec(−t)
For the following exercises, find the values of the six trigonometric functions if the conditions provided hold.cos(2θ) =3/5 and 90° ≤ θ ≤ 180°
For the following exercises, rewrite the product as a sum or difference.sin(3x)cos(5x)
For the following exercises, use the fundamental identities to fully simplify the expression.3 sin3 t csc t + cos2 t + 2 cos(−t)cos t
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. 0 1 2 3 4 5 -3 5 13 5 -3 y 5 6 5
For the following exercises, find the values of the six trigonometric functions if the conditions provided hold.cos(2θ) = 1√2 and 180° ≤ θ ≤ 270°
For the following exercises, use the fundamental identities to fully simplify the expression.−tan(−x)cot(−x)
For the following exercises, simplify to one trigonometric expression. 2 sin (π/4) 2 cos (π/4)
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values. X y -3 -1-√2 -2 -1 -1 1-√2 0 0 1 √2-1 2 1 3 √2+1
For the following exercises, rewrite in terms of sin x and cos x.sin (x −3π/4)
For the following exercises, find all solutions exactly on the interval 0 ≤ θ < 2π.csc2 x − 4 = 0
For the following exercises, use the fundamental identities to fully simplify the expression. -sin(-x)cos x sec xcsc xtan x cot x
For the following exercises, rewrite the sum or difference as a product.sin(3x) + sin(7x)
For the following exercises, simplify to one trigonometric expression. 4 sin (π/8) cos (π/8)
For the following exercises, find the exact values of a) sin(2x), b) cos(2x), and c) tan(2x) without solving for x.If sin x = 1/8 , and x is in quadrant I.
For the following exercises, use the fundamental identities to fully simplify the expression.sin x cos x sec x
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