1.
а) sin13π/6 = sin (2π+π/6 ) = sin π/6 =1/2.
б) tq(-11π/6) = - tq11π/6 = - tq(2π -π/6 ) = tq π/6= √3 / 3.
в) cos4π +ctq 4π/3 = 1 +ctq(π +π/3 ) = 1 +ctq π/3 =1 + √3 / 3.
г) tq π/4 *ctq(- π/4) +cos(3π/2)* sinπ/2 = -tq π/4 *ctq π/4 +0* sinπ/2 = -1.
д) sin405° +cos225°*tq225° = sin(360°+45°) +sin (180°+ 45°) =sin45° -sin45°=0.
2.
а) sin²t - cos²t / ( ctqt *tq(-t) )=sin²t - cos²t /(- ctqt *tqt ) =.sin²t + cos²t =1.
б)
3.
а) cost =1 / 2 . ⇒
t = ± π/3 +2πn , n∈Z.
б) cos(π/2 +t ) = -√3 /2 ⇒ - sin t = -√3 /2 ⇔ sin t = √3 /2 ⇒
t =(-1)^ n * π/3 +πn , n∈Z.
4.
cost =- 4/5 ; π < t < 3π/2 .
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sint - ? ; tqt ? ; ctqt - ?
sint = -√(1-cos²t) = -√(1-(4/5)= -3 /5 ; tqt = sint /cost =(-3/5)/(-4/5) =3/4.
ctqt =1/tqt = 4/3 .
5.
sin(2π -t) -cos(3π/2 +t) +1 = 0 ;
-sint -sint +1 =0 ⇔sint =1/2⇒ t = (-1)^n *( π/6) + πn ,n ∈Z.
* * * { π/6 + 2πn ; (π -π/6) +2πn } ⇔ { π/6 + 2πn ; 5π /6 +2πn } * * *