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mathematics
precalculus
Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions
While driving, Arletha observes the car in front of her with a viewing angle of 22°. If the car is 6 feet wide, how close is Arletha to the car in front of her? Round your answer to one decimal place.
The Washington Monument in Washington, D.C. is 555 feet tall. If a tourist sees the monument with a viewing angle of 8°, how far away, to the nearest foot, is she from the monument?
A forest ranger views a tree that is 200 feet away with a viewing angle of 20°. How tall is the tree to the nearest foot?
An astronomer observes the moon with a viewing angle of 0.52°. If the moon’s average distance from Earth is 384,400 km, what is its radius to the nearest kilometer?
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. Solve: √x + 2√x - 5 = 2
The length L of the chord joining the endpoints of an arc on a circle of radius r subtended by a central angle θ, 0 < θ ≤ π, is given by L =r√2 − 2 cosθ. Use this fact to approximate the field width (the width of scenery the lens can image) of a 450mm camera lens at a distance of 920
If 2 sin2θ+ 3 cos2θ = 3 sinθ cosθ + 1 withθ in quadrant I, find the possible values for cotθ .
If tanθ= 3 − secθ withθ in quadrant I, what is sinθ + cosθ?
If sin(4θ) = cos(2θ) and 0 < 4θ < π/2, find the exact value of sin(8θ) + cot(4θ) − 2.
Find the exact value of sinθ − cosθ if cosθ − 8 sinθ = 7 and 180° < θ < 270°.
Let θ be the measure of an angle, in radians, in standard position with π < θ < 3π/2. Find the exact y-coordinate of the intersection of the terminal side of θ with the unit circle, given cosθ sin2θ = 41/49. State the answer as a single fraction, completely simplified, with
Let θ be the measure of an angle, in radians, in standard position with π/2 < θ < π. Find the exact x -coordinate of the intersection of the terminal side of θ with the unit circle, given cos2θ - sinθ = −1/9. State the answer as a single fraction, completely simplified, with
If the terminal side of an angle contains the point (5n, −12n) with n > 0 , find sinθ.
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Given: f (x) = x2 − 3 and g(x) = x − 7, find (f º g)(x).
How would you explain the meaning of the sine function to a student who has just completed college algebra?
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the difference quotient for 3 = 2x² - − f(x) = - 5x + 1.
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. If g(x) = 1 x² + 1 find f(x) so that f(g(x)) = x² + 1 2
Draw a unit circle. Label the angles 0, π/6, π/4, π/3, . . . , 7π/4, 11π/6, 2π and the coordinates of the points on the unit circle that correspond to each of these angles. Explain how symmetry can be used to find the coordinates of points on the unit circle for angles whose terminal sides
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve exactly: ex−4 = 6
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the domain of f (x) = ln(5x + 2).
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the real zeros of f (x) = x3 − 9x2 + 3x − 27.
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If the polynomial function P(x) = x4 − 5x3 − 9x2 + 155x − 250 has zeros of 4 + 3i and 2, find
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the remainder when P(x) = 8x4 − 2x3 + x − 8 is divided by x + 2.
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If the real zeros of g(x) are −2 and 3, what are the real zeros of g(x + 6)?
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.A sidewalk with a uniform width of 3 feet is to be placed around a circular garden with a diameter
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve: log4 (x − 5) = 2
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the real zeros of f (x) = 3x2 − 7x − 9.
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find c so that f (x) = 6x2 − 28x + c has a minimum value of 7/3.
Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the intercepts of the graph of −3x + 5y = 15.
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If f (x) = x2 − 3 and g(x) = −x + 3, determine where g(x) ≥ f (x).
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve int( x + 3) = −2.
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. If g(x) = x2 4 x2 simplify √1+ [g(x)]².
Answers are given at the end of these exercises. sin(等) (元) ; COS
Answers are given at the end of these exercises. If tan 0 = 12-1 < 0
Problems 146 – 155. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If the point (3, −4) is on the graph of y = f (x) , what corresponding point must be on the graph
Find the exact value of sec2 π/15 − tan2 π/15.
Answers are given at the end of these exercises. 7T (a) sin- 75 (b) tan- n 4 cos= 3 7T sin 6
Answers are given at the end of these exercises. y sec-¹xif and only if and ≤ y ≤- y = 플 EIN ,where[x]
What are the domain and the range of y = sin x?
True or False sin2θ= 1 − cos2θ
Answers are given at the end of these exercises. tan kt k = COST = sin= ; sin =
What are the domain and the range of y = sec x?
Answers are given at the end of these exercises.The distance d from the point (2, −3) to the point (5, 1) is ________.
Answers are given at the end of these exercises. y sin ¹x if and only if 플스 스플 2 and- where -1 ≤ x ≤ 1
Answers are given at the end of these exercises. If sin a lin 5 < a
If the domain of a one-to-one function is [ 3,∞), the range of its inverse is _____.
True or False sin(−θ) + cos(−θ) = cosθ− sinθ
Answers are given at the end of these exercises.If sin θ= 4/5 and θ is in quadrant II, then cosθ= _______.
Find the real solutions of 4x2 − x − 5 = 0.
Ifis a point on the unit circle that corresponds to a real number t, then sin t = ______, cost = ______, and t ant = _______. 1 2√2 3 P = (-1/31
Find the real solutions of x2 − x − 1 = 0.
Answers are given at the end of these exercises.tan2θ− sec2θ= ______ .
Answers are given at the end of these exercises. (a) cos(a + 3) (b) sin(a - 3) = cosa cos sin a cos sin a sin 3 cos a sin 3
Find the real solutions of (2x − 1)2 − 3(2x − 1) − 4 = 0.
True or False The solution set of the equation tanθ = 1 is given by {0|0 = 7 + kπ, k an integer}. {ol
Answers are given at the end of these exercises.The expression 1 1 - sin 0 + 1 1 + sin 0
Answers are given at the end of these exercises.cos(−θ) − cosθ= _____ .
Which of the following equations is not an identity? (a) cot20+1 = csc ²0 Cos (c) tan = sin 0 (b) tan(-0) (d) csc = = - tan 1 sin 0
To find the inverse secant of a real number x , |x| ≥ 1, convert the inverse secant to an inverse ______.
In Problems 9–20, find the exact value of each expression. cot-1√3
Two triangles are if the lengths of two corresponding sides are equal and the angles between the two sides have the same measure.
True or False cos ( 1/2 - 0) = cos
Use a graphing utility to solve 5x3 − 2 = x − x2 . Round answers to two decimal places.
True or False y = tan−1 x if and only if x = tan y, where -∞ < x < ∞ and 1/2 < X < 1/1/201 y
Answers are given at the end of these exercises.sin−1 (sin x) = x for all numbers x for which (a) (c) - - ∞ < x < 0 1 ≤ x ≤ 1 (b) 0 ≤ x ≤ T (d) - / ≤ x ≤ 1/7/2 2
Answers are given at the end of these exercises.cos−1 (cos x) = x for all numbers x for which ______.
In Problems 9–20, find the exact value of each expression. cot-11
True or False The domain of y = cos−1 x is − 1 ≤ x ≤ 1.
True or False If f (x) = sin x and g(x) = cos x, then g(a + 3) = g(a)g(B) - f(a) f(B)
True or False csc−1 0.5 is not defined.
If all solutions of a trigonometric equation are given by the general formula θ = π/6 + 2kπ or θ = 11π/6 + 2kπ, where k is an integer, then which of the following is not a solution of the equation? (a) 35m 6 (b) 23T 6 (c) 13개 6 (d) ㅠ
In Problems 11–20, simplify each trigonometric expression by following the indicated direction.Rewrite in terms of sine and cosine functions: tan csc 0
True or False Two solutions of the equation sinθ= 1/2 are π/6 and 5π/6.
In Problems 9–20, find the exact value of each expression. csc-¹ (-1)
In Problems 11 – 26, find the exact value of each expression. sin-10
True or False sin(sin−1 0) = 0 and c os(cos−1 0) = 0.
True or False tanθ · cosθ= sinθ for any θ ≠ (2k + 1) π/2.
True or False sin(α + β) = sinα + sinβ + 2 sinα sinβ
In Problems 11–20, simplify each trigonometric expression by following the indicated direction.Rewrite in terms of sine and cosine functions: cot sec
In Problems 11 – 26, find the exact value of each expression. cos-11
Choose the expression that completes the Sum Formula for tangent functions: tan(α + β) = ____. (a) (c) tana + tan 3 1 - tanatan 3 tana + tan 3 1+ tanatan 3 (b) (d) tana - tan 3 1+ tanatan 3 tana - tan 3 tanatan 3 1
Suppose θ = π/2 is the only solution of a trigonometric equation in the interval 0 ≤ θ < 2π. Assuming a period of 2π, which of the following formulas gives all solutions of the equation, where k is an integer? (a) 0 = (c) A KIN + 2kπ kπ 2 (b) 0 = (d) = π 2 π + kπ 2 + kr kπ
In Problems 9–20, find the exact value of each expression. csc-1√√√2
In Problems 9–20, find the exact value of each expression. 2√3 3 sec-1;
In Problems 11–20, simplify each trigonometric expression by following the indicated direction. Multiply cose 1 sin 1+ sin 0 1+ sin 0 by.
In Problems 11–20, simplify each trigonometric expression by following the indicated direction. sin 1 + cos 0 Multiply. cos by1-cose
In Problems 11 – 26, find the exact value of each expression. sin-¹ (-1)
In Problems 11 – 26 , find the exact value of each expression. cos-¹(-1)
In Problems 11–20, simplify each trigonometric expression by following the indicated direction.Rewrite as a single quotient: sin + cos cos + cos sin 0 sin 0
In Problems 11 – 26, find the exact value of each expression. tan-¹0
In Problems 13–36, solve each equation on the interval 0 ≤ θ < 2π. 2 sin + 3 = 2
In Problems 9–20, find the exact value of each expression. sec-¹(-2)
In Problems 9–20, find the exact value of each expression. cot-1 (-3)
Choose the expression that is equivalent to sin60°cos20° + cos60°sin20°(a) cos 40°(b) sin 40°(c) cos 80°(d) sin 80°
In Problems 13–24, find the exact value of each expression.cos 165°
In Problems 11–20, simplify each trigonometric expression by following the indicated direction.Rewrite as a single quotient: 1 1 - cos v + 1 1 + cos v
In Problems 13–36, solve each equation on the interval 0 ≤ θ < 2π. 1 - cos || 1 2
In Problems 13–36, solve each equation on the interval 0 ≤ θ < 2π. 2 sin 0+1=0
In Problems 13–24, find the exact value of each expression. 5π 12 sin-
In Problems 9–20, find the exact value of each expression. CSC-1 2√3 3
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