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August 2022 1 14 Report

Вычислите cos(t+4П); ctg(t-3П); tg(t) если sin(t+2П)= -3/5, -П/2<t<0.

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julshum

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$sin(t+2 \pi )=sint=- \frac{3}{5}$
Находим cos t, используя основное тригонометрическое равенство
$cost= \sqrt{1-sin^{2} t}= \sqrt{1- \frac{9}{25} }= \frac{4}{5}$

сos(t+4pi)=cos t=4/5
ctg(t-3pi)=ctg t = cos t/sin t = (4/5)/(-3/5)=- (4*5)/(5*3) = -4/3
tg t = sin t/ cos t = (-3/5)/(4/5)=-(3*5)/(5*4)=-3/4

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