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M1\n- Find the second solution $2x+15=360^\\circ-72.5^\\circ=287.5^\\circ$. M1\n- Rearrange using $x=\\frac{(2x+15)-15}{2}$. M1\n- Obtain $x=28.8^\\circ$. A1\n- Obtain $x=136.2^\\circ$. A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Uses inverse cosine to obtain $2x+15=72.5^\\circ$.","code":"M"},{"id":"p2","marks":1,"description":"Finds the second relevant angle $2x+15=287.5^\\circ$.","code":"M"},{"id":"p3","marks":1,"description":"Rearranges the angle equation correctly to find $x$.","code":"M"},{"id":"p4","marks":1,"description":"Obtains $x=28.8^\\circ$ to one decimal place.","code":"A"},{"id":"p5","marks":1,"description":"Obtains $x=136.2^\\circ$ to one decimal place.","code":"A"}],"finalAnswers":["28.8°","136.2°"],"generatedAt":"2026-08-31T09:28:48.050Z","modelVersion":"cheap:gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":38},"walkthroughVideo":null},{"id":"0cf9904a-5744-40e3-9081-e9d113d11bac","revisionId":"92e2d1df-d19f-4d5e-974b-19229fd98543","questionNumber":null,"questionType":"LA","specification":"","difficultyBand":"medium","tier":null,"totalMarks":6,"sourceTitle":null,"calculatorUse":null,"isCalculation":false,"parts":[{"id":"06c83dd2-3014-4716-91b1-97705c9801c9","label":"a","content":"Sketch the graph of $y=\\sin(x-60)$ for $x$ in the interval $0 \\leq x < 360^\\circ$.","markscheme":"- Sketch a sine curve with amplitude $1$ and period $360^\\circ$. B1\n- Position the curve with zeros at $x=60^\\circ$ and $x=240^\\circ$, a maximum at $(150^\\circ,1)$ and a minimum at $(330^\\circ,-1)$. B1\n\n![Coordinate axes for a sketch of y = sin(x − 60) over 0 ≤ x < 360° and −1 ≤ y ≤ 1.](https://assets.mathsgenie.co.uk/question-variant-figures/v1/24bfbfa62ce27b2c30ee640b5ce1b2ab.svg)","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Sketch a sine curve with amplitude 1 and period 360 degrees.","code":"B","acceptable":["Sine curve with amplitude $1$ and period $360^\\circ$."]},{"id":"p2","marks":1,"description":"Position the zeros and turning points correctly.","code":"B","acceptable":["Zeros at $60^\\circ$ and $240^\\circ$, maximum at $(150^\\circ,1)$ and minimum at $(330^\\circ,-1)$."]}],"finalAnswers":["Sketch of $y=\\sin(x-60)$ with zeros at $60^\\circ$ and $240^\\circ$, maximum at $(150^\\circ,1)$ and minimum at $(330^\\circ,-1)$."],"generatedAt":"2026-09-24T09:31:08.461Z","modelVersion":"gpt-6-sol"},"tableImages":[],"explanation":null,"options":[]},{"id":"82721032-deeb-4ef4-82e0-7f052a5d4d5a","label":"b","content":"Find all values for $x$ in the interval $0 \\leq x < 360^\\circ$ for which\n\n$$\\sin(x - 60) = 0.2$$\n\nGive your answers to one decimal place.","markscheme":"- Use inverse sine to obtain $x-60=\\sin^{-1}(0.2)=11.5^\\circ$. M1\n- Use sine symmetry to obtain the second relevant angle $x-60=168.5^\\circ$. M1\n- Add $60^\\circ$ to both relevant angles. M1\n- Obtain $x=71.5^\\circ$ and $x=228.5^\\circ$. A1","marks":4,"order":1,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Use inverse sine to find the first relevant angle.","code":"M","acceptable":["$$x-60=\\sin^{-1}(0.2)\\approx11.5^\\circ$."]},{"id":"p2","marks":1,"description":"Use sine symmetry to find the second relevant angle.","code":"M","acceptable":["$$x-60=180^\\circ-\\sin^{-1}(0.2)\\approx168.5^\\circ$."]},{"id":"p3","marks":1,"description":"Add 60 degrees to both relevant angles.","code":"M","acceptable":["$$x=60^\\circ+\\sin^{-1}(0.2)$ and $x=240^\\circ-\\sin^{-1}(0.2)$."]},{"id":"p4","marks":1,"description":"Give both values to one decimal place.","code":"A","acceptable":["$$x=71.5^\\circ$ and $x=228.5^\\circ$."]}],"finalAnswers":["$$x=71.5^\\circ$ and $x=228.5^\\circ$"],"generatedAt":"2026-09-24T09:31:08.461Z","modelVersion":"gpt-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":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"0cf9904a-5744-40e3-9081-e9d113d11bac","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"7c6000c2-5567-4836-a8d4-5db8055a602d","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"eb6589f6-6fea-46b1-82fa-c2eef9fe3a93","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"bac9d98c-3ea4-4c39-8a8b-f7bf5b9164c4","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"216b3df2-3815-4367-a58c-a10eafff9923","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"7c79bdee-b62d-4e8c-8f97-f9b92986b151","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"1ca75e72-f052-42da-98b9-6913abf343a3","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"d48db7c8-43c8-43e3-a6b5-1d9f96926b5d","difficultyBand":"easy","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"d9643252-8a73-4755-b03d-2980873cb00b","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"3f1de864-c45b-4f61-bab0-22a1605fa9d9","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"cc4f66f2-dd7e-47c0-9a56-8b864463eba3","difficultyBand":"hard","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"ca799526-b450-438b-bde1-633c20da434e","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"c553ac7c-519e-45a9-8682-9e0b5df60cd3","difficultyBand":"hard","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":false},{"id":"21e8f6af-55e6-4b92-b833-0ca77b054651","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"cc5321e4-7bcb-4b16-82f6-ade9dff16864","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"0efcaa01-0a68-4b37-8f9e-fb220a1fb2b1","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":false},{"id":"f5135238-e04f-4887-8186-d5a944aaf26b","difficultyBand":"medium","calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true}],"title":"10.4 Solving Trigonometric Equations","topicId":"348fe6d1-0ff4-b9b9-a49f-40c4f68ec281","topicSidebar":"$L3a","topicSlug":"as-pure-mathematics-10-4-solving-trigonometric-equations","topicTitle":"10.4 Solving Trigonometric Equations"}]}],"$L3b","$L3c"]}]