7.46.
а) 3cos0 +2sin(π/2)-4cos(π/2) -7sin(-π) =3*1 +2*1 -4*0 -7*0 =5.
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б) cos(π/2) -3sin(-3π/4) +4cos(-2π) -2sin(-3π) =
0 +3sin(3π/4) +4cos(2π) +2sin(3π) =3*(√2)/2 +4*1 +0 =4 +(3/2)*√3.
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7.47.
а) sin(π/4) +cos(-3π/4) -2sin(-π/6) +2cos(5π/6) =
(√2)/2 +cos(3π/4) +2sin(π/6) +2cos(5π/6) =
* * * (√2)/2 -(√2)/2 +2*1/2 -2*(√3)/2 * * *
(√2)/2 +cos(π-π/4) +2sin(π/6) +2cos(π-π/6) =
(√2)/2 -cos(π/4) +2sin(π/6) -2cos(π/6) =
√2)/2 -(√2)/2 +2*1/2 -2*(√3)/2 =1 -√3.
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б) 3cos(π/3) -2sin(2π/3) +7cos(-2π/3) -sin5π/4 =
3*1/2 -2sin(π-π/3) +7cos(2π/3) -sin(π+π/4)=
3*1/2 -2sin(π/3) +7cos(π-π/3) +sin(π/4) =
3*1/2 -2(√3)/2 -7cos(π/3) +(√2)/2 =
3*1/2 -√3 -7*1/2 +(√2)/2 =-2 -√3 + (√2)/2.
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в) 3cos(7π/4)+2sin(3π/4) -sin(9π/4) +7cos(13π/2) =
cos(2π -π/4)+2sin(π-π/4) -sin(2π+π/4) +7cos(6*2π +π/2) =
cos(π/4)+2sin(π/4) -sin(π/4) +7cos(π/2) =cos(π/4)+sin(π/4) -7*0=(√2)/2)+(√2)/2=√2.
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г) 2*sin(-5π/6) +11cos(7π/3) +sin(7π/6) -8cos(2π/3) =
-2*sin(π-π/6) +11cos(2π+π/3) +sin(π+π/6) -8cos(π -π/3) =
-2*sin(π/6) +11cos(π/3) -sin(π/6) +8cos(π/3) =-2*1/2 +11*1/2 -1/2 +8*1/2 =0.