Trigonometry (MindTap Course List)
8th Edition
ISBN: 9781305652224
Author: Charles P. McKeague, Mark D. Turner
Publisher: Cengage Learning
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Chapter 5.3, Problem 64PS
To determine
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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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.
Let sinθ = 2√2/5 and π/2 < θ < πPart A: Determine the exact value of cos 2θ.Part B: Determine the exact value of sin(θ/2)
1. Find the solution set of In(x) sin(x) ≤ 0, for x = [0,14].
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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