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Hilbrain
@Hilbrain
October 2021
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Помогите пожалуйста решить с 1-5
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sedinalana
Verified answer
1
а)y(x)=2x³+tgx
y(-x)=2(-x)³+tg(-x)=-2x³-tgx=-(2x³+tgx)
y(x)=-y(-x) нечетная
б)y(x)=cos^4x*2x^4
y(-x)=cos^4(-x)*2(-x)^4=cos^4x*2x^4
y(x)=y(-x) четная
в)y(x)=tg²x+5x³
y(-x)=tg²(-x)+5(-x)³=tg²x-5x³ ни четная,ни нечетная
2
а)sin225=sin(180+45)=-sin45=-√2/2
б)cos(-135)=cos135=cos(180-45)=-cos45=-√2/2
в)ctg540=ctg(180+60)=ctg60=1/√3
г)tg(-330)=-tg330=-tg(360-30)=-tg(-30)=tg30=1/√3
3
a)(1-cos(3π/2-a)+cos(2π-a))/(1+sin(2π+a)-sin(3π/2+a))=
=(1+sina+cosa)/(1+sina+cosa)=1
б)sin(π/2-a)-cos(π+a)+tg(π-a)-ctg(3π/2+a)=cosa+cosa-tga+tga=2cosa
4
ctg225-ctg675-cos495+cos765=
=ctg(180+45)-ctg(720-45)-cos(360+135)+cos(720+45)=
=ctg45-ctg(-45)-cos135+cos45=ctg45+ctg45-cos(180-45)+cos45=
=2ctg45+cos45+cos45=2*1+√2/2+√2/2=2+√2
5
sina=24/25
cosa=-√(1-sin²a)=-√(1-576/625)=-√(49/625)=-7/25
sin2a=2sinacosa=2*24/25*(-7/25)=-336/625
cos2a=cos²a-sin²a=49/625-576/625=-527/625
tg2a=sin2a/cos2a=-336/625:(-527/625)=336/925*625/527=336/527
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Answers & Comments
Verified answer
1а)y(x)=2x³+tgx
y(-x)=2(-x)³+tg(-x)=-2x³-tgx=-(2x³+tgx)
y(x)=-y(-x) нечетная
б)y(x)=cos^4x*2x^4
y(-x)=cos^4(-x)*2(-x)^4=cos^4x*2x^4
y(x)=y(-x) четная
в)y(x)=tg²x+5x³
y(-x)=tg²(-x)+5(-x)³=tg²x-5x³ ни четная,ни нечетная
2
а)sin225=sin(180+45)=-sin45=-√2/2
б)cos(-135)=cos135=cos(180-45)=-cos45=-√2/2
в)ctg540=ctg(180+60)=ctg60=1/√3
г)tg(-330)=-tg330=-tg(360-30)=-tg(-30)=tg30=1/√3
3
a)(1-cos(3π/2-a)+cos(2π-a))/(1+sin(2π+a)-sin(3π/2+a))=
=(1+sina+cosa)/(1+sina+cosa)=1
б)sin(π/2-a)-cos(π+a)+tg(π-a)-ctg(3π/2+a)=cosa+cosa-tga+tga=2cosa
4
ctg225-ctg675-cos495+cos765=
=ctg(180+45)-ctg(720-45)-cos(360+135)+cos(720+45)=
=ctg45-ctg(-45)-cos135+cos45=ctg45+ctg45-cos(180-45)+cos45=
=2ctg45+cos45+cos45=2*1+√2/2+√2/2=2+√2
5
sina=24/25
cosa=-√(1-sin²a)=-√(1-576/625)=-√(49/625)=-7/25
sin2a=2sinacosa=2*24/25*(-7/25)=-336/625
cos2a=cos²a-sin²a=49/625-576/625=-527/625
tg2a=sin2a/cos2a=-336/625:(-527/625)=336/925*625/527=336/527