N. 117
ա) sin(π/2-α)=cos α
բ) tg(π/2-α)=ctg α
գ) cos(π/2-α)=cos(π/2+(-α))=-sin(-α)=sin α
դ) ctg(α-π)=ctg(-π-α)=-ctg(π-α)=ctg α
ե) tg(α-π)=tg(-π-α)=-tg(π-α)=tg α
զ) cos(3/2×π-α)=-sin α
է) sin(α-3/2×π)=sin(-3/2×π+α)=-sin(3/2×π-α)=cos α
ը) cos(π+α)=-cos α
N. 118
ա) α=210°` sin(210°)=sin(180°+30°)=-sin30°=-1/2; cos(210°)=cos(180°+30°)=-cos30°=-√3/2; tg(210°)=tg(180°+30°)=tg30°=√3/3; ctg(210°)=ctg(180°+30°)=ctg30°=√3
բ) α=5/4×π՝ sin(5/4×π)=sin(225°)=-√2/2; cos(5/4×π)=cos(225°)=-√2/2; tg(5/4×π)=tg(225°)=1; ctg(5/4×π)=ctg(225°)=1
գ) α=4/3×π՝ sin(4/3×π)=sin(240°)=-√3/2; cos(4/3×π)=cos(240°)=-1/2; tg(4/3×π)=tg(240°)=√3; ctg(4/3×π)=ctg(240°)=√3/3
դ) α=300°՝ sin(300°)=-√3/2; cos(300°)=1/2=0,5; tg(300°)=-√3; ctg(300°)=-√3/3
ե) α=9/4×π՝ sin(9/4×π)=√2/2; cos(9/4×π)=√2/2; tg(9/4×π)=1; ctg(9/4×π)=1
զ) α=330°՝ sin(330°)=-1/2=-0,5; cos(330°)=√3/2; tg(330°)=-√3/3; ctg(330°)=-√3
N. 119
ա) ctg(90°-α)=tg α
բ) cos(90°+α)=-sin α
գ) sin(270°-α)=sin(180°+90°-α)=-sin(90°-α)=-cos α
դ) sin(270°+α)=sin(180°+90°+α)=-sin(90°+α)=-cos α
ե) tg(α-270°)=tg(α-180°-90°)=tg(-180°-90°+α)=-tg(180°+90°-α)=tg(90°-α)=-ctg α
զ) ctg(α-180°)=ctg α
N. 120
ա) cos(810°+α)=cos(90°+720°+α)=-sin(720°+α)=-sin α
բ)sin(990°-α)=sin(270°+720°-α)=-cos(720°-α)=-cos α
գ)tg(α-450°)=-ctg α
դ) tg(7π-α)=-tg α
ե) cos(α-13π/2)=cos(α-π/2-6π)=cos(α-π/2)=sin α
զ) ctg(7π/2+α)=ctg(π/2+3π+α)=ctg(π/2+α)=-tg α
N. 121
ա)sin²(π+x)=sin²π+sin²x=sin²x
բ) cos²(3π/2-x)=0+sin²(x)=sin²x
գ) tg²(π+x)=tg²π+tg²x=tg²x
դ) cos⁴(π-x)=-cos⁴(x)=cos⁴x
ե) sin³(3π/2-x)=-cos³x
զ) ctg³(3π/2+x)=-tg³x
N. 122
ա) sin²(180°-α)+sin²(270°-α)=sin²α+(-cos²α)=sin²α+cos²α=1
բ) sin(90°-α)+cos(180°+α)+tg(270°-α)+ctg(360°+α)=sin(90°-α)+cos(180°+α)-ctg α+ctg α=0
գ) sin(π+α)cos(π/2+α)-cos(2π+α)sin(3π/2-α)=-sin α×(-sin α)-cos α×(-cos α)=sin²α+cos²α=1
դ) tg α tg(π/2+α)tg(π+α)tg(3π/2+α)=tg α×(-ctg α)×tg α tg(3π/2+α)=-tgα × ctgα × tgα × (-ctg α)=tg α×1/tg α×tg α×1/tg α=1