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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, find all exact solutions on [0, 2π).2sin(x)cos(x) − sin(x) + 2cos(x) − 1 = 0
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
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
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
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
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
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
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
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
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.

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