Question

Calculati: a)2sin30grade-3tg30grade+4cos60grade=? b)sin40grade-ctg30grade+2cos60grade-cos45grade=?

Answer 1

La 30°, sin=1/2, cos=√3/2, tg=1/√3 si la ctg=√3. La 60°, sin=√3/2, cos=1/2, tg=√3, ctg=1/√3. La 45°, sin=√2/2, cos=√2/3, tg=1, ctg=1. a) 2sin30°-3tg30°+4cos60°=2*1/2-3*√3+4*1/2=1-3*√3+2=3-3√3 b) sin45°-ctg30°+2cos60°-cos45°=√2/2-1/√3+2*1/2-√2/2=1/2

Answer 2

   
$a) \\ 2sin\,30^o-3tg\,30^o+4cos\,60^o = \\ =2\cdot \frac{1}{2} -3\cdot \frac{ \sqrt{3} }{3} +4\cdot \frac{1}{2}=1-\sqrt{3} +2 = \boxed{3-\sqrt{3}} \\ \\ b) \\ sin\,45^o-ctg\,30^o+2cos\,60^o-cos\,45^o= \\ = \frac{ \sqrt{2} }{2} - \sqrt{3} +2\cdot \frac{1}{2} -\frac{ \sqrt{2} }{2}=\frac{ \sqrt{2} }{2}-\frac{ \sqrt{2} }{2} - \sqrt{3}+1= \boxed{1- \sqrt{3}}$