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AlinaBabkunova
@AlinaBabkunova
July 2022
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Решите уравнение 6 cos x + 5cos (пи на 2-x)=7
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hlopushinairina
6cosx+5cos(π/2 -x)=7;
6cosx+5sinx=7;
6cosx=7-5sinx;
36-36sin²x=49-70sinx+25sin²x;
61sin²x-70sinx+13=0;sinx=z;-1≤z≤1;
61z²-70z+13=0;
z₁,₂=(70⁺₋√(4900-4*61*13)/122=(70⁺₋√1728)/122=(70⁺₋41.57)/122;
z₁=(70+41.57)/122=0.914;⇒
sinx=0.914;x=(-1)ⁿarcsin0.914+πn;n∈Z;
z₂=0.233;⇒
sinx=0.233;x=(-1)ⁿarcsin0.233+nπ;n∈Z
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Answers & Comments
6cosx+5sinx=7;
6cosx=7-5sinx;
36-36sin²x=49-70sinx+25sin²x;
61sin²x-70sinx+13=0;sinx=z;-1≤z≤1;
61z²-70z+13=0;
z₁,₂=(70⁺₋√(4900-4*61*13)/122=(70⁺₋√1728)/122=(70⁺₋41.57)/122;
z₁=(70+41.57)/122=0.914;⇒
sinx=0.914;x=(-1)ⁿarcsin0.914+πn;n∈Z;
z₂=0.233;⇒
sinx=0.233;x=(-1)ⁿarcsin0.233+nπ;n∈Z