{"id":340,"date":"2026-02-16T20:53:36","date_gmt":"2026-02-16T20:53:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=340"},"modified":"2026-02-17T20:37:41","modified_gmt":"2026-02-17T20:37:41","slug":"periodic-functions-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/periodic-functions-get-stronger-answer-key\/","title":{"raw":"Periodic Functions: Get Stronger Answer Key","rendered":"Periodic Functions: Get Stronger Answer Key"},"content":{"raw":"

Graphs of the Sine and Cosine Function<\/h1>\r\n1. The sine and cosine functions have the property that [latex]f(x+P)=f(x)[\/latex] for a certain P<\/em>. This means that the function values repeat for every P<\/em> units on the x-axis.\r\n\r\n3. The absolute value of the constant A<\/em> (amplitude) increases the total range and the constant D<\/em> (vertical shift) shifts the graph vertically.\r\n\r\n7. amplitude: [latex]\\frac{2}{3}[\/latex]; period: 2\u03c0; midline: [latex]y=0[\/latex]; maximum: [latex]y=23[\/latex] occurs at [latex]x=0[\/latex]; minimum: [latex]y=\u221223[\/latex] occurs at [latex]x=\\pi[\/latex]; for one period, the graph starts at 0 and ends at 2\u03c0\r\n\"A\r\n\r\n9. amplitude: 4; period: 2\u03c0; midline: [latex]y=0[\/latex]; maximum [latex]y=4[\/latex] occurs at [latex]x=\\frac{\\pi}{2}[\/latex]; minimum: [latex]y=\u22124[\/latex] occurs at [latex]x=\\frac{3\\pi}{2}[\/latex]; one full period occurs from [latex]x=0[\/latex] to [latex]x=2\u03c0[\/latex]\r\n\"A\r\n\r\n11. amplitude: 1; period: \u03c0; midline: y=0; maximum: y=1 occurs at [latex]x=\\pi[\/latex]; minimum: [latex]y=\u22121[\/latex] occurs at [latex]x=\\frac{\\pi}{2}[\/latex]; one full period is graphed from [latex]x=0[\/latex] to [latex]x=\\pi[\/latex]\r\n\"A\r\n\r\n13. amplitude: 4; period: 2; midline: [latex]y=0[\/latex]; maximum: [latex]y=4[\/latex] occurs at [latex]x=0[\/latex]; minimum: [latex]y=\u22124[\/latex] occurs at [latex]x=1[\/latex]\r\n\"A\r\n\r\n15. amplitude: 3; period: [latex]\\frac{\\pi}{4}[\/latex]; midline: [latex]y=5[\/latex]; maximum: [latex]y=8[\/latex] occurs at [latex]x=0.12[\/latex]; minimum: [latex]y=2[\/latex] occurs at [latex]x=0.516[\/latex]; horizontal shift: \u22124; vertical translation 5; one period occurs from [latex]x=0[\/latex] to [latex]x=\\frac{\\pi}{4}[\/latex]\r\n\"A\r\n\r\n17. amplitude: 5; period: [latex]\\frac{2\\pi}{5}; midline: [latex]y=\u22122[\/latex]; maximum: [latex]y=3[\/latex] occurs at [latex]x=0.08[\/latex]; minimum: [latex]y=\u22127[\/latex] occurs at [latex]x=0.71[\/latex]; phase shift:\u22124; vertical translation:\u22122; one full period can be graphed on [latex]x=0[\/latex] to [latex]x=\\frac{2\\pi}{5}[\/latex]\r\n\"A\r\n\r\n19. amplitude: 1; period: 2\u03c0; midline: y=1; maximum:[latex]y=2[\/latex] occurs at [latex]x=2.09[\/latex]; maximum:[latex]y=2[\/latex] occurs at[latex]t=2.09[\/latex]; minimum:[latex]y=0[\/latex] occurs at [latex]t=5.24[\/latex]; phase shift: [latex]\u2212\\frac{\\pi}{3}[\/latex]; vertical translation: 1; one full period is from [latex]t=0[\/latex] to [latex]t=2\u03c0[\/latex]\r\n\"A\r\n\r\n21. amplitude: 1; period: 4\u03c0; midline: [latex]y=0[\/latex]; maximum: [latex]y=1[\/latex] occurs at [latex]t=11.52[\/latex]; minimum: [latex]y=\u22121[\/latex] occurs at [latex]t=5.24[\/latex]; phase shift: \u2212[latex]\\frac{10\\pi}{3}[\/latex]; vertical shift: 0\r\n\"A\r\n\r\n23. amplitude: 2; midline: [latex]y=\u22123[\/latex]; period: 4; equation: [latex]f(x)=2\\sin\\left(\\frac{\\pi}{2}x\\right)\u22123[\/latex]\r\n\r\n25. amplitude: 2; period: 5; midline: [latex]y=3[\/latex]; equation: [latex]f(x)=\u22122\\cos\\left(\\frac{2\\pi}{5}x\\right)+3[\/latex]\r\n\r\n27. amplitude: 4; period: 2; midline: [latex]y=0[\/latex]; equation: [latex]f(x)=\u22124\\cos\\left(\\pi\\left(x\u2212\\frac{\\pi}{2}\\right)\\right)[\/latex]\r\n\r\n29. amplitude: 2; period: 2; midline [latex]y=1[\/latex]; equation: [latex]f(x)=2\\cos\\left(\\frac{\\pi}{x}\\right)+1[\/latex]\r\n\r\n31.\u00a0[latex]\\frac{\\pi}{6},\\frac{5\\pi}{6}[\/latex]\r\n\r\n33.\u00a0[latex]\\frac{\\pi}{4},\\frac{3\\pi}{4}[\/latex]\r\n\r\n35.\u00a0[latex]\\frac{3\\pi}{2}[\/latex]\r\n\r\n37.\u00a0[latex]\\frac{\\pi}{2},\\frac{3\\pi}{2}[\/latex]\r\n\r\n39.\u00a0[latex]\\frac{\\pi}{2},\\frac{3\\pi}{2}[\/latex]\r\n\r\n41.\u00a0[latex]\\frac{\\pi}{6},\\frac{11\\pi}{6}[\/latex]\r\n\r\n47.\r\na. Amplitude: 12.5; period: 10; midline: [latex]y=13.5[\/latex];\r\nb. [latex]h(t)=12.5\\sin\\left(\\frac{\\pi}{5}\\left(t\u22122.5\\right)\\right)+13.5;[\/latex]\r\nc. 26 ft\r\n

Graphs of Other Trigonometric Functions<\/h1>\r\n1. \u00a0Since [latex]y=\\csc x[\/latex] is the reciprocal function of [latex]y=\\sin x[\/latex], you can plot the reciprocal of the coordinates on the graph of [latex]y=\\sin x[\/latex] to obtain the y<\/em>-coordinates of [latex]y=\\csc x[\/latex]. The x<\/em>-intercepts of the graph [latex]y=\\sin x[\/latex] are the vertical asymptotes for the graph of [latex]y=\\csc x[\/latex].\r\n\r\n3.\u00a0Answers will vary. Using the unit circle, one can show that [latex]\\tan(x+\\pi)=\\tan x[\/latex].\r\n\r\n5.\u00a0The period is the same: 2\u03c0.\r\n\r\n6. I\r\n\r\n7. IV\r\n\r\n8. II\r\n\r\n9. III\r\n\r\n11. period: 8; horizontal shift: 1 unit to left\r\n\r\n13. 1.5\r\n\r\n15. 5\r\n\r\n17. [latex]\u2212\\cot x\\cos x\u2212\\sin x[\/latex]\r\n\r\n19.\u00a0stretching factor: 2; period: [latex]\\frac{\\pi}{4}[\/latex]; asymptotes: [latex]x=\\frac{1}{4}\\left(\\frac{\\pi}{2}+\\pi k\\right)+8[\/latex], where k<\/em> is an integer\r\n\"A\r\n\r\n21.\u00a0stretching factor: 6; period: 6; asymptotes: [latex]x=3k[\/latex], where k<\/em> is an integer\r\n\"A\r\n\r\n23.\u00a0stretching factor: 1; period: \u03c0; asymptotes: [latex]x=\u03c0k[\/latex], where k<\/em> is an integer\r\n\"A\r\n\r\n25.\u00a0Stretching factor: 1; period: \u03c0; asymptotes: [latex]x=\\frac{\\pi}{4}+{\\pi}k[\/latex], where k<\/em> is an integer\r\n\"A\r\n\r\n27.\u00a0stretching factor: 2; period: 2\u03c0; asymptotes: [latex]x=\u03c0k[\/latex], where k<\/em> is an integer\r\n\"A\r\n\r\n29.\u00a0stretching factor: 4; period: [latex]\\frac{2\\pi}{3}[\/latex]; asymptotes: [latex]x=\\frac{\\pi}{6}k[\/latex], where k<\/em> is an odd integer\r\n\"A\r\n\r\n31.\u00a0stretching factor: 7; period: [latex]\\frac{2\\pi}{5}[\/latex]; asymptotes: [latex]x=\\frac{\\pi}{10}k[\/latex], where k<\/em> is an odd integer\r\n\"A\r\n\r\n33.\u00a0stretching factor: 2; period: 2\u03c0; asymptotes: [latex]x=\u2212\\frac{\\pi}{4}+\\pi k[\/latex], where k<\/em> is an integer\r\n\"A\r\n\r\n35.\u00a0stretching factor: [latex]\\frac{7}{5}[\/latex]; period: 2\u03c0; asymptotes: [latex]x=\\frac{\\pi}{4}+\\pi[\/latex]k<\/em>, where k<\/em> is an integer\r\n\"A\r\n\r\n37. [latex]y=\\tan\\left(3\\left(x\u2212\\frac{\\pi}{4}\\right)\\right)+2[\/latex]\r\n\"A\r\n\r\n39. [latex]f(x)=\\csc(2x)[\/latex]\r\n\r\n41. [latex]f(x)=\\csc(4x)[\/latex]\r\n\r\n43. [latex]f(x)=2\\csc x[\/latex]\r\n\r\n45. [latex]f(x)=\\frac{1}{2}\\tan(100\\pi x)[\/latex]\r\n\r\n49. [latex]f(x)=\\frac{\\csc(x)}{\\sec(x)}[\/latex]\r\n\r\n55. a. [latex](\u2212\\frac{\\pi}{2}\\text{,}\\frac{\\pi}{2})[\/latex];\r\nb.\r\n\"A\r\nc. [latex]x=\u2212\\frac{\\pi}{2}[\/latex] and [latex]x=\\frac{\\pi}{2}[\/latex]; the distance grows without bound as |x<\/em>| approaches [latex]\\frac{\\pi}{2}[\/latex]\u2014i.e., at right angles to the line representing due north, the boat would be so far away, the fisherman could not see it;\r\nd. 3; when [latex]x=\u2212\\frac{\\pi}{3}[\/latex], the boat is 3 km away;\r\ne. 1.73; when [latex]x=\\frac{\\pi}{6}[\/latex], the boat is about 1.73 km away;\r\nf. 1.5 km; when [latex]x=0[\/latex].\r\n\r\n57. a. [latex]h(x)=2\\tan\\left(\\frac{\\pi}{120}x\\right)[\/latex];\r\nb.\r\n\"An\r\nc. [latex]h(0)=0:[\/latex] after 0 seconds, the rocket is 0 mi above the ground; [latex]h(30)=2:[\/latex] after 30 seconds, the rockets is 2 mi high;\r\nd.\u00a0As x<\/em> approaches 60 seconds, the values of [latex]h(x)[\/latex] grow increasingly large. The distance to the rocket is growing so large that the camera can no longer track it.","rendered":"

Graphs of the Sine and Cosine Function<\/h1>\n

1. The sine and cosine functions have the property that [latex]f(x+P)=f(x)[\/latex] for a certain P<\/em>. This means that the function values repeat for every P<\/em> units on the x-axis.<\/p>\n

3. The absolute value of the constant A<\/em> (amplitude) increases the total range and the constant D<\/em> (vertical shift) shifts the graph vertically.<\/p>\n

7. amplitude: [latex]\\frac{2}{3}[\/latex]; period: 2\u03c0; midline: [latex]y=0[\/latex]; maximum: [latex]y=23[\/latex] occurs at [latex]x=0[\/latex]; minimum: [latex]y=\u221223[\/latex] occurs at [latex]x=\\pi[\/latex]; for one period, the graph starts at 0 and ends at 2\u03c0
\n\"A<\/p>\n

9. amplitude: 4; period: 2\u03c0; midline: [latex]y=0[\/latex]; maximum [latex]y=4[\/latex] occurs at [latex]x=\\frac{\\pi}{2}[\/latex]; minimum: [latex]y=\u22124[\/latex] occurs at [latex]x=\\frac{3\\pi}{2}[\/latex]; one full period occurs from [latex]x=0[\/latex] to [latex]x=2\u03c0[\/latex]
\n\"A<\/p>\n

11. amplitude: 1; period: \u03c0; midline: y=0; maximum: y=1 occurs at [latex]x=\\pi[\/latex]; minimum: [latex]y=\u22121[\/latex] occurs at [latex]x=\\frac{\\pi}{2}[\/latex]; one full period is graphed from [latex]x=0[\/latex] to [latex]x=\\pi[\/latex]
\n\"A<\/p>\n

13. amplitude: 4; period: 2; midline: [latex]y=0[\/latex]; maximum: [latex]y=4[\/latex] occurs at [latex]x=0[\/latex]; minimum: [latex]y=\u22124[\/latex] occurs at [latex]x=1[\/latex]
\n\"A<\/p>\n

15. amplitude: 3; period: [latex]\\frac{\\pi}{4}[\/latex]; midline: [latex]y=5[\/latex]; maximum: [latex]y=8[\/latex] occurs at [latex]x=0.12[\/latex]; minimum: [latex]y=2[\/latex] occurs at [latex]x=0.516[\/latex]; horizontal shift: \u22124; vertical translation 5; one period occurs from [latex]x=0[\/latex] to [latex]x=\\frac{\\pi}{4}[\/latex]
\n\"A<\/p>\n

17. amplitude: 5; period: [latex]\\frac{2\\pi}{5}; midline: [latex]y=\u22122[\/latex]; maximum: [latex]y=3[\/latex] occurs at [latex]x=0.08[\/latex]; minimum: [latex]y=\u22127[\/latex] occurs at [latex]x=0.71[\/latex]; phase shift:\u22124; vertical translation:\u22122; one full period can be graphed on [latex]x=0[\/latex] to [latex]x=\\frac{2\\pi}{5}[\/latex]
\n\"A<\/p>\n

19. amplitude: 1; period: 2\u03c0; midline: y=1; maximum:[latex]y=2[\/latex] occurs at [latex]x=2.09[\/latex]; maximum:[latex]y=2[\/latex] occurs at[latex]t=2.09[\/latex]; minimum:[latex]y=0[\/latex] occurs at [latex]t=5.24[\/latex]; phase shift: [latex]\u2212\\frac{\\pi}{3}[\/latex]; vertical translation: 1; one full period is from [latex]t=0[\/latex] to [latex]t=2\u03c0[\/latex]
\n\"A<\/p>\n

21. amplitude: 1; period: 4\u03c0; midline: [latex]y=0[\/latex]; maximum: [latex]y=1[\/latex] occurs at [latex]t=11.52[\/latex]; minimum: [latex]y=\u22121[\/latex] occurs at [latex]t=5.24[\/latex]; phase shift: \u2212[latex]\\frac{10\\pi}{3}[\/latex]; vertical shift: 0
\n\"A<\/p>\n

23. amplitude: 2; midline: [latex]y=\u22123[\/latex]; period: 4; equation: [latex]f(x)=2\\sin\\left(\\frac{\\pi}{2}x\\right)\u22123[\/latex]<\/p>\n

25. amplitude: 2; period: 5; midline: [latex]y=3[\/latex]; equation: [latex]f(x)=\u22122\\cos\\left(\\frac{2\\pi}{5}x\\right)+3[\/latex]<\/p>\n

27. amplitude: 4; period: 2; midline: [latex]y=0[\/latex]; equation: [latex]f(x)=\u22124\\cos\\left(\\pi\\left(x\u2212\\frac{\\pi}{2}\\right)\\right)[\/latex]<\/p>\n

29. amplitude: 2; period: 2; midline [latex]y=1[\/latex]; equation: [latex]f(x)=2\\cos\\left(\\frac{\\pi}{x}\\right)+1[\/latex]<\/p>\n

31.\u00a0[latex]\\frac{\\pi}{6},\\frac{5\\pi}{6}[\/latex]<\/p>\n

33.\u00a0[latex]\\frac{\\pi}{4},\\frac{3\\pi}{4}[\/latex]<\/p>\n

35.\u00a0[latex]\\frac{3\\pi}{2}[\/latex]<\/p>\n

37.\u00a0[latex]\\frac{\\pi}{2},\\frac{3\\pi}{2}[\/latex]<\/p>\n

39.\u00a0[latex]\\frac{\\pi}{2},\\frac{3\\pi}{2}[\/latex]<\/p>\n

41.\u00a0[latex]\\frac{\\pi}{6},\\frac{11\\pi}{6}[\/latex]<\/p>\n

47.
\na. Amplitude: 12.5; period: 10; midline: [latex]y=13.5[\/latex];
\nb. [latex]h(t)=12.5\\sin\\left(\\frac{\\pi}{5}\\left(t\u22122.5\\right)\\right)+13.5;[\/latex]
\nc. 26 ft<\/p>\n

Graphs of Other Trigonometric Functions<\/h1>\n

1. \u00a0Since [latex]y=\\csc x[\/latex] is the reciprocal function of [latex]y=\\sin x[\/latex], you can plot the reciprocal of the coordinates on the graph of [latex]y=\\sin x[\/latex] to obtain the y<\/em>-coordinates of [latex]y=\\csc x[\/latex]. The x<\/em>-intercepts of the graph [latex]y=\\sin x[\/latex] are the vertical asymptotes for the graph of [latex]y=\\csc x[\/latex].<\/p>\n

3.\u00a0Answers will vary. Using the unit circle, one can show that [latex]\\tan(x+\\pi)=\\tan x[\/latex].<\/p>\n

5.\u00a0The period is the same: 2\u03c0.<\/p>\n

6. I<\/p>\n

7. IV<\/p>\n

8. II<\/p>\n

9. III<\/p>\n

11. period: 8; horizontal shift: 1 unit to left<\/p>\n

13. 1.5<\/p>\n

15. 5<\/p>\n

17. [latex]\u2212\\cot x\\cos x\u2212\\sin x[\/latex]<\/p>\n

19.\u00a0stretching factor: 2; period: [latex]\\frac{\\pi}{4}[\/latex]; asymptotes: [latex]x=\\frac{1}{4}\\left(\\frac{\\pi}{2}+\\pi k\\right)+8[\/latex], where k<\/em> is an integer
\n\"A<\/p>\n

21.\u00a0stretching factor: 6; period: 6; asymptotes: [latex]x=3k[\/latex], where k<\/em> is an integer
\n\"A<\/p>\n

23.\u00a0stretching factor: 1; period: \u03c0; asymptotes: [latex]x=\u03c0k[\/latex], where k<\/em> is an integer
\n\"A<\/p>\n

25.\u00a0Stretching factor: 1; period: \u03c0; asymptotes: [latex]x=\\frac{\\pi}{4}+{\\pi}k[\/latex], where k<\/em> is an integer
\n\"A<\/p>\n

27.\u00a0stretching factor: 2; period: 2\u03c0; asymptotes: [latex]x=\u03c0k[\/latex], where k<\/em> is an integer
\n\"A<\/p>\n

29.\u00a0stretching factor: 4; period: [latex]\\frac{2\\pi}{3}[\/latex]; asymptotes: [latex]x=\\frac{\\pi}{6}k[\/latex], where k<\/em> is an odd integer
\n\"A<\/p>\n

31.\u00a0stretching factor: 7; period: [latex]\\frac{2\\pi}{5}[\/latex]; asymptotes: [latex]x=\\frac{\\pi}{10}k[\/latex], where k<\/em> is an odd integer
\n\"A<\/p>\n

33.\u00a0stretching factor: 2; period: 2\u03c0; asymptotes: [latex]x=\u2212\\frac{\\pi}{4}+\\pi k[\/latex], where k<\/em> is an integer
\n\"A<\/p>\n

35.\u00a0stretching factor: [latex]\\frac{7}{5}[\/latex]; period: 2\u03c0; asymptotes: [latex]x=\\frac{\\pi}{4}+\\pi[\/latex]k<\/em>, where k<\/em> is an integer
\n\"A<\/p>\n

37. [latex]y=\\tan\\left(3\\left(x\u2212\\frac{\\pi}{4}\\right)\\right)+2[\/latex]
\n\"A<\/p>\n

39. [latex]f(x)=\\csc(2x)[\/latex]<\/p>\n

41. [latex]f(x)=\\csc(4x)[\/latex]<\/p>\n

43. [latex]f(x)=2\\csc x[\/latex]<\/p>\n

45. [latex]f(x)=\\frac{1}{2}\\tan(100\\pi x)[\/latex]<\/p>\n

49. [latex]f(x)=\\frac{\\csc(x)}{\\sec(x)}[\/latex]<\/p>\n

55. a. [latex](\u2212\\frac{\\pi}{2}\\text{,}\\frac{\\pi}{2})[\/latex];
\nb.
\n\"A
\nc. [latex]x=\u2212\\frac{\\pi}{2}[\/latex] and [latex]x=\\frac{\\pi}{2}[\/latex]; the distance grows without bound as |x<\/em>| approaches [latex]\\frac{\\pi}{2}[\/latex]\u2014i.e., at right angles to the line representing due north, the boat would be so far away, the fisherman could not see it;
\nd. 3; when [latex]x=\u2212\\frac{\\pi}{3}[\/latex], the boat is 3 km away;
\ne. 1.73; when [latex]x=\\frac{\\pi}{6}[\/latex], the boat is about 1.73 km away;
\nf. 1.5 km; when [latex]x=0[\/latex].<\/p>\n

57. a. [latex]h(x)=2\\tan\\left(\\frac{\\pi}{120}x\\right)[\/latex];
\nb.
\n\"An
\nc. [latex]h(0)=0:[\/latex] after 0 seconds, the rocket is 0 mi above the ground; [latex]h(30)=2:[\/latex] after 30 seconds, the rockets is 2 mi high;
\nd.\u00a0As x<\/em> approaches 60 seconds, the values of [latex]h(x)[\/latex] grow increasingly large. The distance to the rocket is growing so large that the camera can no longer track it.<\/p>\n","protected":false},"author":13,"menu_order":14,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":224,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/340"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/340\/revisions"}],"predecessor-version":[{"id":358,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/340\/revisions\/358"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/224"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/340\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=340"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=340"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=340"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}