Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN: 9781305652224
Author: Charles P. McKeague, Mark D. Turner
Publisher: Cengage Learning
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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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Chapter 5.1, Problem 80PS
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Whether the given equation is an identity or not by graphing the left expression and the right expression together. If so, verify the identity. If not, find a counter example

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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f(θ) = 2sinθ + √2.Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function?Part C: A toddler is jumping on another pogo stick whose length of its spring can be represented by the function g(θ) = 1 cos^2θ + √2. At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.Student AStep 1:1/Cos x * 1/sin x = cot x + tan xStep 2: 1/cos x sin x = cot x + tan xStep 3: (cos^2 x + sin^2 x)/cos x sin x = cot x + tan xStep 4: cos^2 x/cos x sin x + sin^2x/cos x sin x= cot x + tan xStep 5: cos x/sin x + sin x/cos x = cot x + tan xStep 6: cot x + tan x = cot x + tan xStudent BStep 1: sec x csc x = cos x/ sin xStep 2: sec x csc x = cos^2x/cos x sin x + sin^2x/cos x sin xStep 3: sec x csc x = cos^2x + sin^2x/cos x sin xStep 4: sec x csc x = 1/cos x sin xStep 5: sec x csc x = (1/cos x), (1/sin x)Step 6: sec x csc x = sec x csc xPart A: Did either student verify the identity properly? Explain why or why not. Part B: Name two identities that were used in Student A's verification and the steps they appear in.
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Chapter 5 Solutions

Trigonometry (MindTap Course List)

Ch. 5.1 - An identity is a Statement that two expressions...Ch. 5.1 - To prove, or verify, an identity, we start with of...Ch. 5.1 - To prove an identity, it is usually best to start...Ch. 5.1 - If nothing else to mind, try changing everything...Ch. 5.1 - To investigate if an equation is an identity,...Ch. 5.1 - To prove that an equation is not an identity, find...Ch. 5.1 - Factor each expression completely. x2xy sin2sincosCh. 5.1 - Prob. 8PSCh. 5.1 - Prob. 9PSCh. 5.1 - Prob. 10PS
Ch. 5.1 - Multiply the numerator and denominator of the...Ch. 5.1 - Prob. 12PSCh. 5.1 - Prob. 13PSCh. 5.1 - Multiply the numerator and denominator of the...Ch. 5.1 - Prob. 15PSCh. 5.1 - Prob. 16PSCh. 5.1 - Prob. 17PSCh. 5.1 - Prob. 18PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 20PSCh. 5.1 - Prob. 21PSCh. 5.1 - Prob. 22PSCh. 5.1 - Prob. 23PSCh. 5.1 - Prob. 24PSCh. 5.1 - Prob. 25PSCh. 5.1 - Prob. 26PSCh. 5.1 - Prob. 27PSCh. 5.1 - Prob. 28PSCh. 5.1 - Prob. 29PSCh. 5.1 - Prob. 30PSCh. 5.1 - Prob. 31PSCh. 5.1 - Prob. 32PSCh. 5.1 - Prob. 33PSCh. 5.1 - Prob. 34PSCh. 5.1 - Prob. 35PSCh. 5.1 - Prob. 36PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 38PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 40PSCh. 5.1 - Prob. 41PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 43PSCh. 5.1 - Prob. 44PSCh. 5.1 - Prob. 45PSCh. 5.1 - Prob. 46PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 48PSCh. 5.1 - Prob. 49PSCh. 5.1 - Prob. 50PSCh. 5.1 - Prob. 51PSCh. 5.1 - Prob. 52PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 54PSCh. 5.1 - Prob. 55PSCh. 5.1 - Prob. 56PSCh. 5.1 - Prob. 57PSCh. 5.1 - Prob. 58PSCh. 5.1 - Prob. 59PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 62PSCh. 5.1 - Prob. 63PSCh. 5.1 - Prob. 64PSCh. 5.1 - Prob. 65PSCh. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prob. 68PSCh. 5.1 - Prob. 69PSCh. 5.1 - Prob. 70PSCh. 5.1 - Prob. 71PSCh. 5.1 - Prove that each of the following statements is not...Ch. 5.1 - Prove that each of the following statements is not...Ch. 5.1 - Prob. 74PSCh. 5.1 - Prob. 75PSCh. 5.1 - Prob. 76PSCh. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Prob. 78PSCh. 5.1 - Prob. 79PSCh. 5.1 - Prob. 80PSCh. 5.1 - Prob. 81PSCh. 5.1 - Prob. 82PSCh. 5.1 - Prob. 83PSCh. 5.1 - Prob. 84PSCh. 5.1 - Prob. 85PSCh. 5.1 - Prob. 86PSCh. 5.1 - Prob. 87PSCh. 5.1 - Prob. 88PSCh. 5.1 - The problems that follow review material we...Ch. 5.1 - The problems that follow review material we...Ch. 5.1 - Prob. 91PSCh. 5.1 - Prob. 92PSCh. 5.1 - Prob. 93PSCh. 5.1 - Prob. 94PSCh. 5.1 - Prob. 95PSCh. 5.1 - Prob. 96PSCh. 5.1 - Prob. 97PSCh. 5.1 - Prob. 98PSCh. 5.1 - Prob. 99PSCh. 5.1 - Prob. 100PSCh. 5.1 - Prob. 101PSCh. 5.2 - For question 1 through 6, complete each sum or...Ch. 5.2 - For question 1 through 6, complete each sum or...Ch. 5.2 - For question 1 through 6, complete each sum or...Ch. 5.2 - Prob. 4PSCh. 5.2 - Prob. 5PSCh. 5.2 - Prob. 6PSCh. 5.2 - Prob. 7PSCh. 5.2 - Prob. 8PSCh. 5.2 - Prob. 9PSCh. 5.2 - Find exact values for each of the following. cos15Ch. 5.2 - Prob. 11PSCh. 5.2 - Find exact values for each of the following. tan75Ch. 5.2 - Prob. 13PSCh. 5.2 - Prob. 14PSCh. 5.2 - Find exact values for each of the following....Ch. 5.2 - Prob. 16PSCh. 5.2 - Prob. 17PSCh. 5.2 - Prob. 18PSCh. 5.2 - Prob. 19PSCh. 5.2 - Show that each of the following is true....Ch. 5.2 - Prob. 21PSCh. 5.2 - Prob. 22PSCh. 5.2 - Show that each of the following is true....Ch. 5.2 - Prob. 24PSCh. 5.2 - Prob. 25PSCh. 5.2 - Prob. 26PSCh. 5.2 - Prob. 27PSCh. 5.2 - Prob. 28PSCh. 5.2 - Prob. 29PSCh. 5.2 - Prob. 30PSCh. 5.2 - Prob. 31PSCh. 5.2 - Prob. 32PSCh. 5.2 - Write each expression as a single trignometric...Ch. 5.2 - Write each expression as a single trignometric...Ch. 5.2 - Prob. 35PSCh. 5.2 - Prob. 36PSCh. 5.2 - Prob. 37PSCh. 5.2 - Prob. 38PSCh. 5.2 - Prob. 39PSCh. 5.2 - Prob. 40PSCh. 5.2 - Prob. 41PSCh. 5.2 - Prob. 42PSCh. 5.2 - Graph each of the following from x=0 to x=2. Let...Ch. 5.2 - Graph each of the following from x=0 to x=2. Let...Ch. 5.2 - Prob. 45PSCh. 5.2 - Prob. 46PSCh. 5.2 - Prob. 47PSCh. 5.2 - Prob. 48PSCh. 5.2 - Prob. 49PSCh. 5.2 - Graph each of the following from x=0 to x=2. Write...Ch. 5.2 - Prob. 51PSCh. 5.2 - Prob. 52PSCh. 5.2 - Prove each identity. cos(x90)cos(x+90)=2sinxCh. 5.2 - Prob. 54PSCh. 5.2 - Prob. 55PSCh. 5.2 - Prob. 56PSCh. 5.2 - Prob. 57PSCh. 5.2 - Prob. 58PSCh. 5.2 - Prob. 59PSCh. 5.2 - Prob. 60PSCh. 5.2 - Prove each identity. sin(A+B)+sin(AB)=2sinAcosBCh. 5.2 - Prob. 62PSCh. 5.2 - Prob. 63PSCh. 5.2 - Prob. 64PSCh. 5.2 - Prob. 65PSCh. 5.2 - Prob. 66PSCh. 5.2 - Prob. 67PSCh. 5.2 - Prob. 68PSCh. 5.2 - Prob. 69PSCh. 5.2 - Prob. 70PSCh. 5.2 - Prob. 71PSCh. 5.2 - Prob. 72PSCh. 5.2 - Prob. 73PSCh. 5.2 - Prob. 74PSCh. 5.2 - Prob. 75PSCh. 5.2 - Prob. 76PSCh. 5.2 - Prob. 77PSCh. 5.2 - Prob. 78PSCh. 5.2 - Prob. 79PSCh. 5.2 - Prob. 80PSCh. 5.2 - Prob. 81PSCh. 5.2 - Prob. 82PSCh. 5.2 - Prob. 83PSCh. 5.3 - For Questions 1 through 3, complete each...Ch. 5.3 - Prob. 2PSCh. 5.3 - Prob. 3PSCh. 5.3 - Prob. 4PSCh. 5.3 - Prob. 5PSCh. 5.3 - Prob. 6PSCh. 5.3 - Let A=35 with A in QIII and find the following....Ch. 5.3 - Prob. 8PSCh. 5.3 - Let A=35 with A in QIII and find the following....Ch. 5.3 - Let A=35 with A in QIII and find the following....Ch. 5.3 - Let cosx=34 with x in QIV and find the following....Ch. 5.3 - Let cosx=34 with x in QIV and find the following....Ch. 5.3 - Let cosx=34 with x in QIV and find the following....Ch. 5.3 - Prob. 14PSCh. 5.3 - Let tan=3 with in QI and find the following. sin2Ch. 5.3 - Let tan=3 with in QI and find the following. cos2Ch. 5.3 - Let tan=3 with in QI and find the following. sec2Ch. 5.3 - Prob. 18PSCh. 5.3 - Prob. 19PSCh. 5.3 - Prob. 20PSCh. 5.3 - Let csc=5 with t in QII and find the following....Ch. 5.3 - Let csc=5 with t in QII and find the following....Ch. 5.3 - Prob. 23PSCh. 5.3 - Prob. 24PSCh. 5.3 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Prob. 26PSCh. 5.3 - Prob. 27PSCh. 5.3 - Prob. 28PSCh. 5.3 - Prob. 29PSCh. 5.3 - Prob. 30PSCh. 5.3 - Use exact values to show that each of the...Ch. 5.3 - Prob. 32PSCh. 5.3 - Prob. 33PSCh. 5.3 - Use exact values to show that each of the...Ch. 5.3 - Simplify each of the following. 2sin15cos15Ch. 5.3 - Simplify each of the following. cos2165sin2165Ch. 5.3 - Simplify each of the following. 12sin275Ch. 5.3 - Prob. 38PSCh. 5.3 - Simplify each of the following. sin12cos12Ch. 5.3 - Prob. 40PSCh. 5.3 - Simplify each of the following. tan22.51tan222.5Ch. 5.3 - Simplify each of the following. tan112.51tan2112.5Ch. 5.3 - Prob. 43PSCh. 5.3 - Prob. 44PSCh. 5.3 - Prob. 45PSCh. 5.3 - Prob. 46PSCh. 5.3 - Prove each of the following identities....Ch. 5.3 - Prove each of the following identities....Ch. 5.3 - Prob. 49PSCh. 5.3 - Prove each of the following identities....Ch. 5.3 - Prove each of the following identities....Ch. 5.3 - Prob. 52PSCh. 5.3 - Prove each of the following identities....Ch. 5.3 - Prob. 54PSCh. 5.3 - Prob. 55PSCh. 5.3 - Prove each of the following identities....Ch. 5.3 - Prob. 57PSCh. 5.3 - Prove each of the following identities....Ch. 5.3 - Prob. 59PSCh. 5.3 - Prob. 60PSCh. 5.3 - Prob. 61PSCh. 5.3 - Prob. 62PSCh. 5.3 - Prob. 63PSCh. 5.3 - Prob. 64PSCh. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Prob. 66PSCh. 5.3 - Prob. 67PSCh. 5.3 - Prob. 68PSCh. 5.3 - Prob. 69PSCh. 5.3 - Prob. 70PSCh. 5.3 - Prob. 71PSCh. 5.3 - Prob. 72PSCh. 5.3 - Prob. 73PSCh. 5.3 - Prob. 74PSCh. 5.3 - Prob. 75PSCh. 5.3 - Prob. 76PSCh. 5.3 - Prob. 77PSCh. 5.3 - Prob. 78PSCh. 5.4 - For Questions 1 and 2, fill in the blank with an...Ch. 5.4 - Prob. 2PSCh. 5.4 - For Questions 3 through 5, complete each...Ch. 5.4 - Prob. 4PSCh. 5.4 - Prob. 5PSCh. 5.4 - For Questions 6 through 8, determine if the...Ch. 5.4 - Prob. 7PSCh. 5.4 - Prob. 8PSCh. 5.4 - If 0A90, then A/2 terminates in which quadrant?Ch. 5.4 - If 90A180, then A/2 terminates in which quadrant?Ch. 5.4 - If 180A270, then A/2 terminates in which quadrant?Ch. 5.4 - Prob. 12PSCh. 5.4 - If 270A360, then is cos(A/2) positive or negative?Ch. 5.4 - If 180A270, then is sin(A/2) positive or negative?Ch. 5.4 - True or false: If sinA is positive, then sin(A/2)...Ch. 5.4 - True or false: If cosA is negative, then cos(A/2)...Ch. 5.4 - Prob. 17PSCh. 5.4 - Prob. 18PSCh. 5.4 - Prob. 19PSCh. 5.4 - Use half-angle formulas to find the exact values...Ch. 5.4 - Use half-angle formulas to find the exact values...Ch. 5.4 - Prob. 22PSCh. 5.4 - Prob. 23PSCh. 5.4 - NOTE For the following problems, assume that all...Ch. 5.4 - Prob. 25PSCh. 5.4 - Prob. 26PSCh. 5.4 - If sinA=513 with A in QII, find the following....Ch. 5.4 - Prob. 28PSCh. 5.4 - If sinA=513 with A in QII, find the following....Ch. 5.4 - If sinA=513 with A in QII, find the following....Ch. 5.4 - If sinB=13 in QIII, find the following. sinB2Ch. 5.4 - If sinB=13 in QIII, find the following. cscB2Ch. 5.4 - If sinB=13 in QIII, find the following. cosB2Ch. 5.4 - Prob. 34PSCh. 5.4 - If sinB=13 in QIII, find the following. cotB2Ch. 5.4 - If sinB=13 in QIII, find the following. tanB2Ch. 5.4 - If sinA=45 with A in QII, and sinB=35 with B in...Ch. 5.4 - If sinA=45 with A in QII, and sinB=35 with B in...Ch. 5.4 - If sinA=45 with A in QII, and sinB=35 with B in...Ch. 5.4 - If sinA=45 with A in QII, and sinB=35 with B in...Ch. 5.4 - Graph each of the following from x=0 to x=4....Ch. 5.4 - Prob. 42PSCh. 5.4 - Prob. 43PSCh. 5.4 - Prob. 44PSCh. 5.4 - Prob. 45PSCh. 5.4 - Prove the following identities. 2cos22=sin21cosCh. 5.4 - Prob. 47PSCh. 5.4 - Prove the following identities. csc2A2=2secAsecA1Ch. 5.4 - Prob. 49PSCh. 5.4 - Prove the following identities....Ch. 5.4 - Prove the following identities. tanx2+cotx2=2cscxCh. 5.4 - Prob. 52PSCh. 5.4 - Prob. 53PSCh. 5.4 - Prob. 54PSCh. 5.4 - Prob. 55PSCh. 5.4 - Prob. 56PSCh. 5.4 - Prob. 57PSCh. 5.4 - Prob. 58PSCh. 5.4 - Prob. 59PSCh. 5.4 - The following problems review material we covered...Ch. 5.4 - Prob. 61PSCh. 5.4 - Prob. 62PSCh. 5.4 - Prob. 63PSCh. 5.4 - Prob. 64PSCh. 5.4 - Prob. 65PSCh. 5.4 - Prob. 66PSCh. 5.4 - Prob. 67PSCh. 5.4 - Prob. 68PSCh. 5.4 - Prob. 69PSCh. 5.5 - For Questions 1 and 2, fill in the blank with an...Ch. 5.5 - Prob. 2PSCh. 5.5 - Prob. 3PSCh. 5.5 - Prob. 4PSCh. 5.5 - Prob. 5PSCh. 5.5 - Prob. 6PSCh. 5.5 - Prob. 7PSCh. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Prob. 10PSCh. 5.5 - Prob. 11PSCh. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Prob. 13PSCh. 5.5 - Prob. 14PSCh. 5.5 - Prob. 15PSCh. 5.5 - Prob. 16PSCh. 5.5 - Prob. 17PSCh. 5.5 - Write each expression as an equivalent algebric...Ch. 5.5 - Prob. 19PSCh. 5.5 - Prob. 20PSCh. 5.5 - Prob. 21PSCh. 5.5 - Write each expression as an equivalent algebric...Ch. 5.5 - Prob. 23PSCh. 5.5 - Prob. 24PSCh. 5.5 - Prob. 25PSCh. 5.5 - Prob. 26PSCh. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Prob. 28PSCh. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Prob. 32PSCh. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Prob. 35PSCh. 5.5 - Prob. 36PSCh. 5.5 - Prob. 37PSCh. 5.5 - Prob. 38PSCh. 5.5 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Prob. 40PSCh. 5.5 - Prob. 41PSCh. 5.5 - Prob. 42PSCh. 5.5 - Prob. 43PSCh. 5.5 - Prob. 44PSCh. 5.5 - Prob. 45PSCh. 5.5 - Prob. 46PSCh. 5.5 - Verify each identity. tan4x=sin5x+sin3xcos3x+cos5xCh. 5.5 - Prob. 48PSCh. 5.5 - Prob. 49PSCh. 5.5 - Prob. 50PSCh. 5.5 - Prob. 51PSCh. 5.5 - Prob. 52PSCh. 5.5 - Prob. 53PSCh. 5.5 - Prob. 54PSCh. 5.5 - Prob. 55PSCh. 5.5 - Prob. 56PSCh. 5.5 - Prob. 57PSCh. 5.5 - Prob. 58PSCh. 5 - Prove each identity. cotcsc=cosCh. 5 - Prob. 2CTCh. 5 - Prove each identity. seccos=tansinCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Let sinA=35 with 270A360 and cosB=817 with 90B180...Ch. 5 - Let sinA=35 with 270A360 and cosB=817 with 90B180...Ch. 5 - Prob. 15CTCh. 5 - Let sinA=35 with 270A360 and cosB=817 with 90B180...Ch. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 24CTCh. 5 - Prob. 25CTCh. 5 - Prob. 26CTCh. 5 - Prob. 27CTCh. 5 - Prob. 28CTCh. 5 - Prob. 29CTCh. 5 - Prob. 30CTCh. 5 - Prob. 1GPCh. 5 - Prob. 2GPCh. 5 - Prob. 3GPCh. 5 - Prob. 4GPCh. 5 - Prob. 5GPCh. 5 - Prob. 1RP
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Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY