Найдите все значения [-п;п] sinx=корень3/2 cosx=корень 2/2. Created by wais99. algebra-ru

1) sinx=√3/2 ∉[-π; π] - не подходитОтвет: π/3; 2π/3Ответ: -π/4; π/4

2...

June 2022 1 8 Report

Найдите все значения
[-п;п] sinx=корень3/2
cosx=корень 2/2

Answers & Comments

m11m 1) sinx=√3/2
$x=(-1)^{k}* \frac{ \pi }{3}+ \pi k \\ 
 \\ 
k=1 \\ 
x=- \frac{ \pi }{3}- \pi = \frac{-4 \pi }{3}$ ∉[-π; π] - не подходит

$k=0 \\ 
x=(-1)^0* \frac{ \pi }{3}+ \pi *0= \frac{ \pi }{3} \\ 
 \\ 
k=1 \\ 
x=(-1)^1* \frac{ \pi }{3}+ \pi *1=- \frac{p}{3}+ \pi = \frac{2 \pi }{3} \\$

Ответ: π/3; 2π/3

$2) cosx= \frac{ \sqrt{2} }{2} \\ 
x=(+/-) \frac{ \pi }{4}+2 \pi k \\ 

$

$a) x= \frac{ \pi }{4}+2 \pi k \\ 
k=0 \\ 
x= \frac{ \pi }{4} \\ 
 \\ 
b) x= - \frac{ \pi }{4}+2 \pi k \\ 
k=0 \\ 
x=- \frac{ \pi }{4}$

Ответ: -π/4; π/4

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