smilequi9653
15.12.2019 •
Mathematics
Consider the equation 3 cos 2x + sin x = 1
(a) write this equation in the form f(x) = 0, where f(x) = a sin^2 x + b sin x + c
(b) factor f(x)
(c) write down the number of solutions of f(x) = 0, for 0 < x < 2π (do not solve 0)
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Ответ:
→3 cos 2x + sin x− 1=0
i.e 3 {1−2sin²x} + sin x− 1=0
→ 3 −6sin²x + sin x− 1=0
→ −6sin²x + sin x+2=0
→f(x) = −6sin²x + sin x+2=0 where p= −6, q=1 and r=2
f(x) = −6sin²x + sin x+2= −6sin²x +4 sin x−3sinx+2
=−2sinx(3sinx −2)−(3sinx−2)
=(3sinx −2)(−2sinx−1) =−(3sinx −2)(2sinx+1)
f(x) = −6sin²x + sin x+2=0
=−(3sinx −2)(2sinx+1)=0
Either (3sinx −2) =0 i. sinx =2/3 or (2sinx+1)=0 →sinx=−1/2
0 ≤ x ≤ 2π there are two solutions for sinx =2/3
x= 41.81° and 138.19°
and another two solutions for sinx=− 1/2
x= 210° 330°
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Ответ:
pi/3 letter b
did it on e2020