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M1\n- Use the $180^\\circ$ period of tangent to obtain the other relevant angle $111.8^\\circ$. M1\n- Subtract $30^\\circ$ from the relevant angles. M1\n- Obtain $\\theta=-98.2^\\circ$ and $\\theta=81.8^\\circ$. A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Uses inverse tangent to obtain $\\theta+30=-68.2^\\circ$.","code":"M"},{"id":"p2","marks":1,"description":"Uses the tangent period to obtain the other relevant angle $111.8^\\circ$.","code":"M"},{"id":"p3","marks":1,"description":"Subtracts $30^\\circ$ from the relevant angles.","code":"M"},{"id":"p4","marks":1,"description":"Gives both solutions $\\theta=-98.2^\\circ$ and $\\theta=81.8^\\circ$.","code":"A"}],"finalAnswers":["-98.2°","81.8°"],"generatedAt":"2026-08-31T09:28:48.050Z","modelVersion":"cheap:gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"216b3df2-3815-4367-a58c-a10eafff9923","revisionId":"b91601cd-ccf9-43d7-bcac-a8161a5f813c","questionNumber":"4","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":4,"sourceTitle":"10.4 Solving Trigonometric Equations","calculatorUse":null,"isCalculation":true,"parts":[{"id":"292d1b19-6edc-45c2-a1d9-f3ade24554a7","label":"","content":"Solve, for $0 \\leq x < 360^\\circ$, the equation\n\n$$5\\cos(x - 40) = 2$$\n\nGive your answers to two decimal places.","markscheme":"- Rearrange to obtain $\\cos(x-40)=0.4$. M1\n- Use inverse cosine and cosine symmetry to obtain $x-40=66.4^\\circ$ or $293.6^\\circ$. M1\n- Add $40^\\circ$ to the relevant angles. M1\n- Obtain $x=106.42^\\circ$ and $x=333.58^\\circ$. A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Rearranges the equation to $\\cos(x-40)=0.4$.","code":"M"},{"id":"p2","marks":1,"description":"Uses inverse cosine and cosine symmetry to obtain both relevant angles for $x-40$.","code":"M","acceptable":["$$66.4^\\circ$ and $293.6^\\circ$"]},{"id":"p3","marks":1,"description":"Adds $40^\\circ$ to the relevant angles.","code":"M"},{"id":"p4","marks":1,"description":"Gives both solutions $x=106.42^\\circ$ and $x=333.58^\\circ$.","code":"A"}],"finalAnswers":["106.42°","333.58°"],"generatedAt":"2026-08-31T09:28:48.050Z","modelVersion":"cheap:gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"1ca75e72-f052-42da-98b9-6913abf343a3","revisionId":"cd9781d4-f085-4c2e-a773-98c5b5946b29","questionNumber":"5","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":5,"sourceTitle":"10.4 Solving Trigonometric Equations","calculatorUse":null,"isCalculation":true,"parts":[{"id":"f8ca1c9c-92c9-4cec-94ca-9aa8cca5857a","label":"","content":"Solve, for $0 \\leq x < 360^\\circ$, the equation\n\n$$\\tan^2(x) = 3$$","markscheme":"- Take square roots to obtain $\\tan x=\\pm\\sqrt{3}$. M1\n- Solve $\\tan x=\\sqrt{3}$ using an inverse tangent. M1\n- Obtain $x=60^\\circ$ and $x=240^\\circ$ from the positive case. A1\n- Solve $\\tan x=-\\sqrt{3}$ using the tangent period. M1\n- Obtain the complete solution set $x=60^\\circ$, $120^\\circ$, $240^\\circ$ and $300^\\circ$. A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Takes both square roots to obtain $\\tan x=\\pm\\sqrt{3}$.","code":"M"},{"id":"p2","marks":1,"description":"Uses inverse tangent to solve $\\tan x=\\sqrt{3}$.","code":"M"},{"id":"p3","marks":1,"description":"Obtains $x=60^\\circ$ and $x=240^\\circ$ from $\\tan x=\\sqrt{3}$.","code":"A"},{"id":"p4","marks":1,"description":"Uses inverse tangent and periodicity to solve $\\tan x=-\\sqrt{3}$.","code":"M"},{"id":"p5","marks":1,"description":"Gives the complete solution set $x=60^\\circ,120^\\circ,240^\\circ,300^\\circ$.","code":"A"}],"finalAnswers":["60°","120°","240°","300°"],"generatedAt":"2026-08-31T09:28:48.050Z","modelVersion":"cheap:gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"a_level_maths","summaries":[{"id":"f91b9054-8f4c-4d6d-ac5a-81425f223f36","difficultyBand":null,"calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"7c6000c2-5567-4836-a8d4-5db8055a602d","difficultyBand":null,"calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"bac9d98c-3ea4-4c39-8a8b-f7bf5b9164c4","difficultyBand":null,"calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"216b3df2-3815-4367-a58c-a10eafff9923","difficultyBand":null,"calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"1ca75e72-f052-42da-98b9-6913abf343a3","difficultyBand":null,"calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"d9643252-8a73-4755-b03d-2980873cb00b","difficultyBand":null,"calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"cc4f66f2-dd7e-47c0-9a56-8b864463eba3","difficultyBand":null,"calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"c553ac7c-519e-45a9-8682-9e0b5df60cd3","difficultyBand":null,"calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":false},{"id":"cc5321e4-7bcb-4b16-82f6-ade9dff16864","difficultyBand":null,"calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"0efcaa01-0a68-4b37-8f9e-fb220a1fb2b1","difficultyBand":null,"calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":false},{"id":"f5135238-e04f-4887-8186-d5a944aaf26b","difficultyBand":null,"calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true}],"title":"10.4 Solving Trigonometric Equations","topicId":"348fe6d1-0ff4-b9b9-a49f-40c4f68ec281","topicSidebar":"$L3c","topicSlug":"as-pure-mathematics-10-4-solving-trigonometric-equations","topicTitle":"10.4 Solving Trigonometric Equations"}]}],"$L3d","$L3e"]}]