[{"data":1,"prerenderedAt":112},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Ftrigonometria\u002Fangulos-en-posicion-normal?{}":3,"topics-with-content:trigonometria":98},{"course":4,"topic":12,"counts":16,"universities":21,"channels":32,"sampleQuestions":54,"sameName":97},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},4,"trigonometria","Trigonometría","Trig.","math","i-lucide-radius",3,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":11},404,"angulos-en-posicion-normal","Ángulos en posición normal",{"topicId":13,"courseId":5,"questions":17,"classes":18,"videos":19,"minutes":20},7,44,37,897,[22,28],{"universityId":23,"questions":5,"years":24},1,[25,26,27],2026,2024,2022,{"universityId":29,"questions":11,"years":30},2,[25,31,26],2025,[33,36,39,42,44,46,48,50,52],{"name":34,"classes":35},"Alberto Cruz",13,{"name":37,"classes":38},"Academia Grupo Ciencias",9,{"name":40,"classes":41},"Academia ipluton",8,{"name":43,"classes":5},"Ciclo Uni-San Marcos",{"name":45,"classes":5},"Salón Sapiens",{"name":47,"classes":29},"CEPRE UNMSM",{"name":49,"classes":29},"Pamer Corporación Educativa",{"name":51,"classes":23},"Academias Aduni y César Vallejo",{"name":53,"classes":23},"META VILLARREAL",[55,80],{"id":56,"courseId":5,"topicId":13,"pastExamId":57,"stem":58,"options":59,"correctKey":61,"explanation":75,"difficulty":11,"status":76,"source":77,"stats":78},1657,198,"Sean los ángulos α y β positivos y menores que una vuelta, si sus lados finales se ubican respectivamente en el IIC y IVC. Indique el cuadrante en el que se ubica el lado final del ángulo\n$\\dfrac{3\\beta-4\\alpha}{8}$",[60,63,66,69,72],{"key":61,"text":62},"A","IC",{"key":64,"text":65},"B","IIC",{"key":67,"text":68},"C","IIIC",{"key":70,"text":71},"D","IVC",{"key":73,"text":74},"E","el ángulo es cuadrantal","","published","UNI 2026-1 · Matemática",{"attempts":79,"accuracy":79},0,{"id":81,"courseId":5,"topicId":13,"pastExamId":82,"stem":83,"options":84,"correctKey":67,"explanation":75,"difficulty":5,"status":76,"source":95,"stats":96},5418,254,"Se tiene dos ángulos cuyas medidas son θ y β, y han sido medidos en el sentido del movimiento de las manecillas del reloj. El ángulo de medida θ está en el segundo cuadrante y el de medida β en el primer cuadrante. Si $\\operatorname{sen}\\theta=\\dfrac{9}{41}$ y $\\tan\\beta=\\dfrac{40}{9}\\tan\\theta-\\dfrac{9}{10}\\operatorname{ctg}\\theta$, halle $P=-\\dfrac{3}{\\sqrt{10}}\\csc\\beta+\\dfrac{4}{\\sqrt{10}}\\sec\\beta$.",[85,87,89,91,93],{"key":61,"text":86},"2",{"key":64,"text":88},"−5",{"key":67,"text":90},"3",{"key":70,"text":92},"−3",{"key":73,"text":94},"5","UNMSM 2026-I · Medicina Humana",{"attempts":79,"accuracy":79},[],[99,100,101,13,102,103,104,105,106,107,108,109,110,111],401,402,403,405,406,407,408,409,410,411,412,413,414,1791501527727]