Date | May 2017 | Marks available | 7 | Reference code | 17M.1.sl.TZ2.7 |
Level | SL only | Paper | 1 | Time zone | TZ2 |
Command term | Solve | Question number | 7 | Adapted from | N/A |
Question
Solve log2(2sinx)+log2(cosx)=−1, for 2π<x<5π2.
Markscheme
correct application of loga+logb=logab (A1)
eglog2(2sinxcosx), log2+log(sinx)+log(cosx)
correct equation without logs A1
eg2sinxcosx=2−1, sinxcosx=14, sin2x=12
recognizing double-angle identity (seen anywhere) A1
eglog(sin2x), 2sinxcosx=sin2x, sin2x=12
evaluating sin−1(12)=π6 (30∘) (A1)
correct working A1
egx=π12+2π, 2x=25π6, 29π6, 750∘, 870∘, x=π12and x=5π12, one correct final answer
x=25π12, 29π12 (do not accept additional values) A2 N0
[7 marks]
Examiners report
[N/A]
Syllabus sections
Topic 3 - Circular functions and trigonometry » 3.5 » Solving trigonometric equations in a finite interval, both graphically and analytically.
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