Question

Дано: sin(4π+t)=3/5, 0<t<π/2. Вычислите tg(π-t).

Answer 1

sin(4π+t)=3/5,
0<t<π/2
tg(π-t)-?
sin(4π+t)=sint=3/5
tg(π-t)=-tgt
-tgt=-sint/cost
cos=√1-sin²t=√1-9/25=√16/25
cost=4/5
-tgt=-3/5*5/4=-3/4

Answer 2

Sin(4π + t) = 3/5
Sint = 3/5
Cost = + - √(1 - Sin²t)
Так как t - угол первой четверти, то
Cost = √(1 - Sin²t) = √( 1 - 9/25) = √16/25 = 4/5
tg(π - t) = - tgt = - Sint/Cost = - 3/5 : 4/5 = - 3/4 = - 0,75