Solutions for MAT 171 ACCESS CODE
Problem 4SP:
Evaluate sin30 , cos30 , and tan30 .Problem 6SP:
For each function value, find a cofunction with the same value. a. tan22.5=21 b. sec3=2Problem 7SP:
Suppose that a farm worker determines that the distance along the ground from her position to the...Problem 8SP:
If a 15-ft ladder is leaning against a wall at an angle of 62 with the ground, how high up the wall...Problem 1PE:
In a right triangle with an acute angle the longest side in the triangle is the and is opposite...Problem 2PE:
The leg of a right triangle that lies on one ray of angle is called the leg, and the leg that lies...Problem 5PE:
Given the lengths of two sides of a right triangle, we can find the length of the third side by...Problem 6PE:
An right triangle is a right triangle in which the two legs are of equal length. The two acute...Problem 7PE:
The length of the shorter leg of a 306090 triangle is always the length of the hypotenuse.Problem 8PE:
For the six trigonometric functions sin,cos,tan,csc,sec, and cot, identify the three reciprocal...Problem 9PE:
tan is the of sin and cos .Problem 11PE:
The two acute angles in a right triangle are complementary because the sum of their measures is .Problem 12PE:
The sine of angle equals the cosine of . For this reason, the sine and cosine functions are called...Problem 13PE:
For Exercises 13-14, find the exact values of the six trigonometric functions for angle .Problem 14PE:
For Exercises 13-14, find the exact values of the six trigonometric functions for angle .Problem 15PE:
For Exercises 15-18, first use the Pythagorean theorem to find the length of the missing side. Then...Problem 16PE:
For Exercises 15-18, first use the Pythagorean theorem to find the length of the missing side. Then...Problem 18PE:
For Exercises 15-18, first use the Pythagorean theorem to find the length of the missing side. Then...Problem 19PE:
For Exercises 19-22, first use the Pythagorean theorem to find the length of the missing side of the...Problem 20PE:
For Exercises 19-22, first use the Pythagorean theorem to find the length of the missing side of the...Problem 23PE:
In Exercises 23-24, given the value of one trigonometric function of an acute angle , find the...Problem 24PE:
In Exercises 23-24, given the value of one trigonometric function of an acute angle , find the...Problem 25PE:
For Exercises 25-30, assume that is an acute angle. (See Example 2) If cos=217 , find csc .Problem 26PE:
For Exercises 25-30, assume that is an acute angle. (See Example 2) If sin=1717 , find cot .Problem 28PE:
For Exercises 25-30, assume that is an acute angle. (See Example 2) If csc=3 , find cos .Problem 30PE:
For Exercises 25-30, assume that is an acute angle. (See Example 2) If cot=32 , find cos .Problem 32PE:
a. Evaluate sin60 . b. Evaluate sin30+sin30 . c. Are the values in parts (a) and (b) the same?Problem 33PE:
For Exercises 33-38, find the exact value of each expression without the use of a calculator. (See...Problem 34PE:
For Exercises 33-38, find the exact value of each expression without the use of a calculator. (See...Problem 36PE:
For Exercises 33-38, find the exact value of each expression without the use of a calculator. (See...Problem 37PE:
For Exercises 33-38, find the exact value of each expression without the use of a calculator. (See...Problem 38PE:
For Exercises 33-38, find the exact value of each expression without the use of a calculator. (See...Problem 41PE:
For Exercises 39-44, determine whether the statement is true or false for an acute angle by using...Problem 44PE:
For Exercises 39-44, determine whether the statement is true or false for an acute angle by using...Problem 45PE:
For Exercises 45-50, given the function value, find a cofunction of another angle with the same...Problem 46PE:
For Exercises 45-50, given the function value, find a cofunction of another angle with the same...Problem 48PE:
For Exercises 45-50, given the function value, find a cofunction of another angle with the same...Problem 49PE:
For Exercises 45-50, given the function value, find a cofunction of another angle with the same...Problem 50PE:
For Exercises 45-50, given the function value, find a cofunction of another angle with the same...Problem 51PE:
For Exercises 51-54, use a calculator to approximate the function values to 4 decimal places. Be...Problem 52PE:
For Exercises 51-54, use a calculator to approximate the function values to 4 decimal places. Be...Problem 53PE:
For Exercises 51-54, use a calculator to approximate the function values to 4 decimal places. Be...Problem 54PE:
For Exercises 51-54, use a calculator to approximate the function values to 4 decimal places. Be...Problem 55PE:
An observer at the top of a 426-ft cliff measures the angle of depression from the top of a cliff to...Problem 56PE:
A lamppost casts a shadow of 18ft when the angle of elevation of the Sun is 33.7 . How high is the...Problem 57PE:
A 30-ft boat ramp makes a 7 angle with the water. What is the height of the ramp above the water at...Problem 59PE:
The Lookout Mountain Incline Railway, located in Chattanooga, Tennessee, is 4972ft long and runs up...Problem 60PE:
A 12-ft ladder learning against a house makes a 64 angle with the ground. Will the ladder reach a...Problem 61PE:
According to National Football League (NFL) rules, all crossbars on goalposts must be 10ft from the...Problem 62PE:
A zip line is to be built between two towers labeled A and B across a wetland area. To approximate...Problem 63PE:
To determine the width of a river from point A to point B , a surveyor walks downriver 50ft along a...Problem 64PE:
For Exercises 64-68, use the fundamental trigonometric identities as needed. Given that sinx0.3746 ,...Problem 65PE:
For Exercises 64-68, use the fundamental trigonometric identities as needed. Give that cosx0.6691 ,...Problem 66PE:
For Exercises 64-68, use the fundamental trigonometric identities as needed. Given thatcos12=2+64 ,...Problem 67PE:
For Exercises 64-68, use the fundamental trigonometric identities as needed. Given that tan36=525 ,...Problem 70PE:
An airplane traveling 400 mph at a cruising altitude of 6.6 mi begins its descent. If the angle of...Problem 71PE:
A scientist standing at the top of a mountain 2mi above sea level measures the angle of depression...Problem 73PE:
Find the exact lengths x,y , and z .Problem 74PE:
Use the figure to explain why tan=cot90 .Problem 76PE:
An athlete is in a boat at point A, 14mi from the nearest point D on a straight shoreline. She can...Problem 78PE:
In the figure, CD=15,DE=8,tan=43 and sin=35 , Find the lengths of a. AC b. AD c. DB d. BE e. ABProblem 81PE:
Use a cofunction relationship to show that the product tan1tan2tan3tan87tan88tan89 is equal to 1 .Problem 82PE:
For Exercises 82-85, use a calculator to approximate the values of the left- and right-hand sides of...Browse All Chapters of This Textbook
Chapter R - Review Of PrerequisitesChapter R.1 - Sets And The Real Number LineChapter R.2 - Exponents And RadicalsChapter R.3 - Polynomials And FactoringChapter R.4 - Rational Expressions And More Operations On RadicalsChapter R.5 - Equations With Real SolutionsChapter R.6 - Complex Numbers And More Quadratic EquationsChapter R.7 - Applications Of EquationsChapter R.8 - Linear, Compound, And Absolute Value InequalitiesChapter 1 - Functions And Relations
Chapter 1.1 - The Rectangular Coordinate System And Graphing UtilitiesChapter 1.2 - CirclesChapter 1.3 - Functions And RelationsChapter 1.4 - Linear Equations In Two Variables And Linear FunctionsChapter 1.5 - Applications Of Linear Equations And ModelingChapter 1.6 - Transformations Of GraphsChapter 1.7 - Analyzing Graphs Of Functions And Piecewise-defined FunctionsChapter 1.8 - Algebra Of Functions And Function CompositionChapter 2 - Polynomial And Rational FunctionsChapter 2.1 - Quadratic Functions And ApplicationsChapter 2.2 - Introduction To Polynomial FunctionsChapter 2.3 - Division Of Polynomials And The Remainder And Factor TheoremsChapter 2.4 - Zeros Of PolynomialsChapter 2.5 - Rational FunctionsChapter 2.6 - Polynomial And Rational InequalitiesChapter 2.7 - VariationChapter 3 - Exponential And Logarithmic FunctionsChapter 3.1 - Inverse FunctionsChapter 3.2 - Exponential FunctionsChapter 3.3 - Logarithmic FunctionsChapter 3.4 - Properties Of LogarithmsChapter 3.5 - Exponential And Logarithmic Equations And ApplicationsChapter 3.6 - Modeling With Exponential And Logarithmic FunctionsChapter 4 - Trigonometric FunctionsChapter 4.1 - Angles And Their MeasureChapter 4.2 - Trigonometric Functions Defined On The Unit CircleChapter 4.3 - Right Triangle TrigonometryChapter 4.4 - Trigonometric Functions Of Any AngleChapter 4.5 - Graphs Of Sine And Cosine FunctionsChapter 4.6 - Graphs Of Other Trigonometric FunctionsChapter 4.7 - Inverse Trigonometric FunctionsChapter 5 - Analytic TrigonometryChapter 5.1 - Fundamental Trigonometric IdentitiesChapter 5.2 - Sum And Difference FormulasChapter 5.3 - Double-angle, Power-reducing, And Half-angle FormulasChapter 5.4 - Product-to-sum And Sum-to-product FormulasChapter 5.5 - Trigonometric EquationsChapter 6 - Applications Of Trigonometric FunctionsChapter 6.1 - Applications Of Right TrianglesChapter 6.2 - The Law Of SinesChapter 6.3 - The Law Of CosinesChapter 6.4 - Harmonic MotionChapter 7 - Trigonometry Applied To Polar Coordinate Systems And VectorsChapter 7.1 - Polar CoordinatesChapter 7.2 - Graphs Of Polar EquationsChapter 7.3 - Complex Numbers In Polar FormChapter 7.4 - VectorsChapter 7.5 - Dot ProductChapter 8 - Systems Of Equations And InequalitiesChapter 8.1 - Systems Of Linear Equations In Two Variables And ApplicationsChapter 8.2 - Systems Of Linear Equations In Three Variables And ApplicationsChapter 8.3 - Partial Fraction DecompositionChapter 8.4 - Systems Of Nonlinear Equations In Two VariablesChapter 8.5 - Inequalities And Systems Of Inequalities In Two VariablesChapter 8.6 - Linear ProgrammingChapter 9 - Matrices And Determinants And ApplicationsChapter 9.1 - Solving Systems Of Linear Equations Using MatricesChapter 9.2 - Inconsistent Systems And Dependent EquationsChapter 9.3 - Operations On MatricesChapter 9.4 - Inverse Matrices And Matrix EquationsChapter 9.5 - Determinants And Cramer’s RuleChapter 10 - Analytic GeometryChapter 10.1 - The EllipseChapter 10.2 - The HyperbolaChapter 10.3 - The ParabolaChapter 10.4 - Rotation Of AxesChapter 10.5 - Polar Equations Of ConicsChapter 10.6 - Plane Curves And Parametric EquationsChapter 11 - Sequences, Series, Induction, And ProbabilityChapter 11.1 - Sequences And SeriesChapter 11.2 - Arithmetic Sequences And SeriesChapter 11.3 - Geometric Sequences And SeriesChapter 11.4 - Mathematical InductionChapter 11.5 - The Binomial TheoremChapter 11.6 - Principles Of CountingChapter 11.7 - Introduction To Probability
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