Algebra and Trigonometry
Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 8, Problem 28PT

For the following exercises, graph the functions on the specified window and answer the questions.

28. Graph f ( x ) = s i n x x on [ − 0.5 , 0.5 ] and explain why observations.

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Chapter 8 Solutions

Algebra and Trigonometry

Ch. 8.1 - Determine the period of the function g(x)=(cosx3)...Ch. 8.1 - What is the amplitude of the sinusoidal function...Ch. 8.1 - Determine the direction and magnitude of the phase...Ch. 8.1 - Determine the direction and magnitude of the...Ch. 8.1 - Determine the midline, amplitude, period, and...Ch. 8.1 - Determine the formula for the sine function in...Ch. 8.1 - Write a formula for the function graphed in figure...Ch. 8.1 - Sketch a graph of g(x)=0.8cos(2x) . Determine the...Ch. 8.1 - Draw a graph of g(x)=2cos(3x+6) . Determine the...Ch. 8.1 - What is the amplitude of the function f(x)=7cos(x)...
Ch. 8.1 - A weight is attached to a spring that is then hung...Ch. 8.1 - Why are the sine and cosine functions called...Ch. 8.1 - How does the graph of y=sinx compare with the...Ch. 8.1 - For the equation Acos(Bx+C)+D, what constants...Ch. 8.1 - How does the range of a translated sine function...Ch. 8.1 - How can the unit circle be used to construct the...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - Determine the amplitude, midline, period, and an...Ch. 8.1 - Determine the amplitude, period, midline and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - For the following exercises, let f(x)=sinx . 31....Ch. 8.1 - For the following exercises, let f(x)=sinx . 32....Ch. 8.1 - For the following exercises, let f(x)=sinx . 33....Ch. 8.1 - For the following exercises, let f(x)=sinx . 34....Ch. 8.1 - For the following exercises, let f(x)=sinx . 35....Ch. 8.1 - For the following exercises, let f(x)=sinx . 36....Ch. 8.1 - For the following exercises, let f(x)=sinx . 37....Ch. 8.1 - For the following exercises, let f(x)=cosx. 38. On...Ch. 8.1 - For the following exercises, let f(x)=cosx. 39. On...Ch. 8.1 - For the following exercises, let f(x)=cosx. 40. On...Ch. 8.1 - For the following exercises, let f(x)=cosx. 41. On...Ch. 8.1 - For the following exercises, let f(x)=cosx 42. On...Ch. 8.1 - Graph h(x)=x+sinx on [0,2) . Explain why the graph...Ch. 8.1 - Graph h(x)=x+sinx on [100,100] . Did the graph...Ch. 8.1 - Graph f(x)=x+sinx on [0,2) and verbalize how the...Ch. 8.1 - Graph f(x)=x+sinx on the window [10,10] and...Ch. 8.1 - Graph f(x)=sinxx on the window [5,5] and explain...Ch. 8.1 - A Ferris wheel is 25 meters in diameter and...Ch. 8.2 - Sketch a graph of f(x)=3tan(6x) .Ch. 8.2 - How would the graph in Example 2 look different if...Ch. 8.2 - Find a formula for the function in Figure 5.Ch. 8.2 - Graph one period of f(x)=2.5sec(0.4x) .Ch. 8.2 - Graph one period of f(x)=6sec(4x+2)8 .Ch. 8.2 - Graph one period of f(x)=0.5csc(2x) .Ch. 8.2 - Given the graph of f(x)=2cos(2x)+1 shown in Figure...Ch. 8.2 - Explain how the graph of the sine function can be...Ch. 8.2 - How can the graph of y=cosx be used to construct...Ch. 8.2 - Explain why the period of tan x is equal .Ch. 8.2 - Why are there no intercepts on the graph of...Ch. 8.2 - How does the period of y=cscx compare with the...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, rewrite each...Ch. 8.2 - For the following exercises, rewrite each...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, find and graph two...Ch. 8.2 - For the following exercises, find and graph two...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - The function f(x)=20tan(10x) marks the distance in...Ch. 8.2 - Standing on the shore of a lake, a fisherman...Ch. 8.2 - A laser rangefinder is locked on a comet...Ch. 8.2 - A video camera is focused on a rocket on a...Ch. 8.3 - Given cos(0.5)0.8776 , write a relation involving...Ch. 8.3 - Evaluate each of the following. a. sin1(1) b....Ch. 8.3 - Evaluate cos1(0.4) using a calculator.Ch. 8.3 - Solve the triangle in Figure 9 for the angle .Ch. 8.3 - Evaluate tan1(tan(8)) and tan1(tan( 119)) .Ch. 8.3 - Evaluate cos1(sin( 114)) .Ch. 8.3 - Evaluate cos(tan1(5 12)) .Ch. 8.3 - Evaluate cos(sin1(79)) .Ch. 8.3 - Find a simplified expression for sin(tan1(4x)) for...Ch. 8.3 - Why do the functions f(x)=sin1x and g(x)=cos1x...Ch. 8.3 - Since the function y=cosx and y=cos1x are inverse...Ch. 8.3 - Explain the meaning of 6=arcsin(0.5) .Ch. 8.3 - Most calculators do not have a key to evaluate...Ch. 8.3 - Why must the domain of the sine function, sin x,...Ch. 8.3 - Discuss why this statement is incorrect:...Ch. 8.3 - Determine whether the following statement is true...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, find the angle in...Ch. 8.3 - For the following exercises, find the angle in...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - Graph y=sin1x and state the domain and range of...Ch. 8.3 - Graph y=arccosx and state the domain and range of...Ch. 8.3 - Graph one cycle of y=tan1x and state the domain...Ch. 8.3 - For what value of x does sinx=sin1x ? Use a...Ch. 8.3 - For what value of x does cosx=cos1x ? Use a...Ch. 8.3 - Suppose a 13-foot ladder is leaning against a...Ch. 8.3 - Suppose you drive 0.6 miles on a road so that the...Ch. 8.3 - An isosceles triangle has two congruent sides of...Ch. 8.3 - Without using a calculator, approximate the value...Ch. 8.3 - A truss for the roof of a house is constructed...Ch. 8.3 - The line y=35x passes through the origin in the...Ch. 8.3 - The line y=37x passes through the origin in the...Ch. 8.3 - What percentage grade should a road have if the...Ch. 8.3 - A 20-foot ladder leans up against the side of a...Ch. 8.3 - Suppose a 15-foot ladder leans against the side of...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - Graph f(x)=cosxand f(x)=secx on the interval [0,2)...Ch. 8 - Graph f(x)=sinx and f(x)=cscx and explain any...Ch. 8 - Graph the function f(x)=x1x33!+x55!x77! on the...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, determine the...Ch. 8 - For the following exercises, determine the...Ch. 8 - For the following exercises, determine the...Ch. 8 - For the following exercises, find the amplitude,...Ch. 8 - For the following exercises, find the amplitude,...Ch. 8 - The outside temperature over the course of a day...Ch. 8 - Water is pumped into a storage bin and empties...Ch. 8 - For the following exercises, find the period and...Ch. 8 - For the following exercises, find the period and...Ch. 8 - Write the equation for the graph in Figure 1 in...Ch. 8 - If tanx=3 , find tan(x) .Ch. 8 - If secx=4 , find sec(x) .Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, let f(x)=35cos(6x) ....Ch. 8 - For the following exercises, let f(x)=35cos(6x) ....Ch. 8 - For the following exercises, let f(x)=35cos(6x) ....Ch. 8 - For the following exercises, find and graph one...Ch. 8 - For the following exercises, find and graph one...Ch. 8 - For the following exercises, graph the function....Ch. 8 - For the following exercises, graph the function....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, suppose sint=xx+1 ....Ch. 8 - For the following exercises, suppose sint=xx+1 ....Ch. 8 - Given Figure 2, find the measure of angle to...Ch. 8 - For the following exercises, determine whether the...Ch. 8 - For the following exercises, determine whether the...Ch. 8 - The grade of a road is 7%. This means that for...
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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY