Question

a) Stiind ca sin 80* - cos 80* = a, sa se calculeze sin 100* + cos 100* - a
b) Sa se calculeze numarul sin 60* x cos 150 *
c) Sa se calculeze sin 135* + tg 45* - cos 45*

* = grade
x = inmultit(ori)

Answer 1

In general, sin(y*)=sin(180*-y*) si cos(y*)=-cos(180*-y*).
La toate subpunctele vom folosi aceste doua formule.

a)
sin100*+cos100*-a=sin(180*-100*)-cos(180*-100*)-a=sin80*-cos80*-a=a-a=0.

b)
sin60* x cos150* = sin60* x (-cos(180*-150*))=-sin60* x cos30*=-(rad(3)/2)*(rad(3)/2)=-3/4.

c)
sin135*+tg45*-cos45* = sin(180*-135*)+tg45*-cos45*=sin45*+tg45*-cos45*=
=rad(2)/2+1-rad(2)/2=1.