Question

Oblicz:
a) cos 13π/6 * sin 4π/3 + tg 7π/4 *cos 5π/3
b) ctg 5π/6 * sin 2π/3 - tg 7π/3 * cos 5π/2

Answer 1

Oblicz:
a) cos 13π/6 * sin 4π/3 + tg 7π/4 *cos 5π/3
cos (2π +π/6) * sin (π+π/3) + tg(π +π/4) *cos (2π-π/3)=
cos (π/6) * (-sin (π/3)) + tg(π/4) *cos (π/3)=
√3 /2 * (-√3 /2) + 1 *1/2=
-3/4 + 1/2=-3/4 + 2/4=-1/4


b) ctg 5π/6 * sin 2π/3 - tg 7π/3 * cos 5π/2=
ctg (2π-π/6) * sin(π- π/3) - tg(2π+ π/3) * cos (2π+π/2)=
(-ctg (π/6) )* sin(π/3) - tg( π/3) * cos (π/2)=
(-√3 )* √3 /2 - √3 * 0=
-3 /2 -0=-3 /2

Answer 2

A)
cos 13π/6 * sin 4π/3 + tg 7π/4 *cos 5π/3 =
cos (2π+π/6) * sin (π+π/3) + tg (2π-π/4) *cos (2π-π/3) =
cos π/6 * (-sin π/3) + tg (-π/4) * cos (-π/3) =
sin(π/2 - π/6)* (-sin π/3) - tg π/4 * cos π/3 =
-sin² π/3 - 1 * ½ = -(√3/2)² - ½ = -¾ - ½ = -⁵/₄ = -1,25

b)
ctg 5π/6 * sin 2π/3 - tg 7π/3 * cos 5π/2 =
ctg (π-π/6) * sin (π-π/3) - tg (2π+π/3) * cos (2π+π/2) =
ctg (-π/6) * sin π/3 - tg π/3 * cos π/2 =
-ctg π/6 * sin π/3 - tg π/3 * 0 =
-1/tg π/6 * √3/2 = -√3 * √3/2 = -½*3 = -1,5