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TrigonometryTrigonometry (MindTap Course List)8th Edition
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Write each expression as a single trignometric function. cos 15 ° cos 75 ° − sin 15 ° sin 75 °

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Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
Publisher: Cengage Learning
ISBN: 9781305652224

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Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
Publisher: Cengage Learning
ISBN: 9781305652224
Chapter 5.2, Problem 33PS
Textbook Problem
1 views

Write each expression as a single trignometric function.

cos 15 ° cos 75 ° − sin 15 ° sin 75 °

To determine

To write:

The given expression as a single trigonometric function.

Explanation of Solution

Given information:

cos5xcosx−sin5xsinx

Formula Used:

cosAcosB−sinAsinB=cos(A+B)

cos90°=0

Calculation:

Steps Description
cos15°cos75°−sin15°sin75°cosAcosB−sinAsinB⇒A=15°;    B=75° We need to compare our expressio

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Trigonometry (MindTap Course List)
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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 - Factor each expression completely. 1y2 1cos2Ch. 5.1 - Factor each expression completely. x2y2 cos2sin2Ch. 5.1 - Factor each expression completely. x4y4 sin4cos4
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Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 5.1 - Prove that each of the following identities is...Ch. 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 - Prove that each of the following statements is not...Ch. 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 - Prove that each of the following statements is not...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - Use your graphing calculator to determine if each...Ch. 5.1 - The following identities are from the book Plane...Ch. 5.1 - The following identities are from the book Plane...Ch. 5.1 - The following identities are from the book Plane...Ch. 5.1 - The following identities are from the book Plane...Ch. 5.1 - The problems that follow review material we...Ch. 5.1 - The problems that follow review material we...Ch. 5.1 - Give the exact value of each of the following....Ch. 5.1 - Give the exact value of each of the following....Ch. 5.1 - Give the exact value of each of the following....Ch. 5.1 - Give the exact value of each of the following....Ch. 5.1 - Convert the degrees. 12Ch. 5.1 - Convert the degrees. 59Ch. 5.1 - Prove each identity. 97. csc+sin()=cos2sinCh. 5.1 - Prove each identity. 98. seccos()=sin2cosCh. 5.1 - The questions are available for instructors to...Ch. 5.1 - The questions are available for instructors to...Ch. 5.1 - The questions are available for instructors to...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 - 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 - For question 1 through 6, complete each sum or...Ch. 5.2 - For Questions 7 and 8, determine if the statement...Ch. 5.2 - For Questions 7 and 8, determine if the statement...Ch. 5.2 - Find exact values for each of the following. sin15Ch. 5.2 - Find exact values for each of the following. cos15Ch. 5.2 - Find exact values for each of the following. tan15Ch. 5.2 - Find exact values for each of the following. tan75Ch. 5.2 - Find exact values for each of the following....Ch. 5.2 - 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Graph...Ch. 5.2 - Graph each of the following from x=0 to x=2. Graph...Ch. 5.2 - Graph each of the following from x=0 to x=2. Graph...Ch. 5.2 - Graph each of the following from x=0 to x=2. Graph...Ch. 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 - Graph each of the following from x=0 to x=2. If...Ch. 5.2 - Graph each of the following from x=0 to x=2. If...Ch. 5.2 - Graph each of the following from x=0 to x=2. If...Ch. 5.2 - Graph each of the following from x=0 to x=2. If...Ch. 5.2 - Graph each of the following from x=0 to x=2. Write...Ch. 5.2 - Graph each of the following from x=0 to x=2. 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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 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Graph each of the following from x=0 to x=2....Ch. 5.3 - Use exact values to show that each of the...Ch. 5.3 - Use exact values to show that each of the...Ch. 5.3 - Use exact values to show that each of the...Ch. 5.3 - Use exact values to show that each of the...Ch. 5.3 - Use exact values to show that each of the...Ch. 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 - Simplify each of the following. 2cos21051Ch. 5.3 - Simplify each of the following. sin12cos12Ch. 5.3 - 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Prove each of the following identities....Ch. 5.3 - Prove each of the following identities....Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - Use your graphing calculator to determine if each...Ch. 5.3 - The problems that follow review material we...Ch. 5.3 - The problems that follow review material we...Ch. 5.3 - The problems that follow review material we...Ch. 5.3 - The problems that follow review material we...Ch. 5.3 - Graph each of the following from x=0 to x=8....Ch. 5.3 - Graph each of the following from x=0 to x=8....Ch. 5.3 - These questions are available for instructors to...Ch. 5.3 - These questions are available for instructors to...Ch. 5.3 - These questions are available for instructors to...Ch. 5.3 - These questions are available for instructors to...Ch. 5.4 - For Questions 1 and 2, fill in the blank with an...Ch. 5.4 - For Questions 1 and 2, fill in the blank with an...Ch. 5.4 - For Questions 3 through 5, complete each...Ch. 5.4 - For Questions 3 through 5, complete each...Ch. 5.4 - For Questions 3 through 5, complete each...Ch. 5.4 - For Questions 6 through 8, determine if the...Ch. 5.4 - For Questions 6 through 8, determine if the...Ch. 5.4 - For Questions 6 through 8, determine if the...Ch. 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 - If 270A360, then A/2 terminates in which quadrant?Ch. 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 - Use half-angle formulas to find the exact values...Ch. 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 - Use half-angle formulas to find the exact values...Ch. 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 - NOTE For the following problems, assume that all...Ch. 5.4 - NOTE For the following problems, assume that all...Ch. 5.4 - NOTE For the following problems, assume that all...Ch. 5.4 - NOTE For the following problems, assume that all...Ch. 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 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 - 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Prove the following identities. tanx2cotx2=2cotxCh. 5.4 - Prove the following identities. cos22=tan+sin2tanCh. 5.4 - Prove the following identities. 2sin22=sin21+cosCh. 5.4 - Prove the following identities....Ch. 5.4 - Prove the following identities. 4sin4=12cos2+cos22Ch. 5.4 - Navigation As we have seen in previous chapters,...Ch. 5.4 - The following problems review material we covered...Ch. 5.4 - The following problems review material we covered...Ch. 5.4 - The following problems review material we covered...Ch. 5.4 - The following problems review material we covered...Ch. 5.4 - Write an equivalent algebric expression that...Ch. 5.4 - Write an equivalent algebric expression that...Ch. 5.4 - Write an equivalent algebric expression that...Ch. 5.4 - Write an equivalent algebric expression that...Ch. 5.4 - These questions are available for instructors to...Ch. 5.4 - These questions are available for instructors to...Ch. 5.4 - These questions are available for instructors to...Ch. 5.4 - In proving the identity cos22=tan+sin2tan, which...Ch. 5.5 - For Questions 1 and 2, fill in the blank with an...Ch. 5.5 - For Questions 1 and 2, fill in the blank with an...Ch. 5.5 - For Question 3 and 4, complete each product to sum...Ch. 5.5 - For Question 3 and 4, complete each product to sum...Ch. 5.5 - For Question 5 and 6, complete each sum to product...Ch. 5.5 - For Question 5 and 6, complete each sum to product...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Evaluate each expression Without using a...Ch. 5.5 - Write each expression as an equivalent algebric...Ch. 5.5 - Write each expression as an equivalent algebric...Ch. 5.5 - Write each expression as an equivalent algebric...Ch. 5.5 - Write each expression as an equivalent algebric...Ch. 5.5 - 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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 - 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 - Rewrite each expression as a sum or difference,...Ch. 5.5 - Verify each identity. cotx=sin3x+sinxcos3xcosxCh. 5.5 - Verify each identity. cotx=cos3x+cosxsin3xsinxCh. 5.5 - Verify each identity. cot2x=sin3xsinxcosxcos3xCh. 5.5 - Verify each identity. cotx=sin4x+sin6xcos4xcos6xCh. 5.5 - Verify each identity. tan4x=sin5x+sin3xcos3x+cos5xCh. 5.5 - Verify each identity. tan4x=cos3xcos5xsin3xsin5xCh. 5.5 - The problems that follow review material we...Ch. 5.5 - The problems that follow review material we...Ch. 5.5 - The problems that follow review material we...Ch. 5.5 - The problems that follow review material we...Ch. 5.5 - The problems that follow review material we...Ch. 5.5 - The problems that follow review material we...Ch. 5.5 - These questions are available for instructors to...Ch. 5.5 - These questions are available for instructors to...Ch. 5.5 - These questions are available for instructors to...Ch. 5.5 - These questions are available for instructors to...Ch. 5 - Prove each identity. cotcsc=cosCh. 5 - Prove each identity. (secx1)(secx+1)=tan2xCh. 5 - Prove each identity. seccos=tansinCh. 5 - Prove each identity. cost1sint=1+sintcostCh. 5 - Prove each identity. 11sint+11+sint=2sec2tCh. 5 - Prove each identity. cos(2+)=sinCh. 5 - Prove each identity. cos4Asin4A=cos2ACh. 5 - Prove each identity. cotA=sin2A1cos2ACh. 5 - Prove each identity. cotxtanx=cos2xsinxcosxCh. 5 - Prove each identity. tanx2=tanxsecx+1Ch. 5 - Use your graphing calculator to determine if each...Ch. 5 - Use your graphing calculator to determine if each...Ch. 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 - Let sinA=35 with 270A360 and cosB=817 with 90B180...Ch. 5 - Let sinA=35 with 270A360 and cosB=817 with 90B180...Ch. 5 - Find exact values for each of the following. sin75Ch. 5 - Find exact values for each of the following. cos12Ch. 5 - Write each expression as a single trigonometric...Ch. 5 - Write each expression as a single trigonometric...Ch. 5 - Write each expression as a single trigonometric...Ch. 5 - Write each expression as a single trigonometric...Ch. 5 - Write each expression as a single trigonometric...Ch. 5 - Write each expression as a single trigonometric...Ch. 5 - Evaluate each expression Now without using a...Ch. 5 - Evaluate each expression Now without using a...Ch. 5 - Write each expression as an equivalent algebric...Ch. 5 - Write each expression as an equivalent algebric...Ch. 5 - Write each expression as an equivalent algebric...Ch. 5 - Write each expression as an equivalent algebric...Ch. 5 - Graph y=sinx+cosx with your graphing calculator....Ch. 5 - First, we will assume asinBx+bcosBx=Asin(Bx+C)....Ch. 5 - Solve for A in terms of a and b using the...Ch. 5 - Write y=sinx+cosx in the form y=Asin(Bx+C). First...Ch. 5 - Graph your equation from Question 4 and it with...Ch. 5 - Many of the identities presented in this chapter...

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