how to solve, with solution

Question

2cos 150°-3sin 90° +tan 210°

Answer 1

sine(90 deg)=1....-3 sine(90)=-3

kosine(150)=-0.8660254037844387

2*kosine=-1.7320508075688774...-sqrt(3)

tan(210 deg)=0.5773502691896254...sqrt(3)/3

yu hav -sqrt(3) -3 +sqrt(3)/3   or(-2/3)*sqrt(3) -3

become -3 -1.1547005383792514

=-4.1547005383792514

Answer 2

To find the related angles of given ones, and their (+) or (-) signs, use the unit circle.

cos150°= cos(180°- 30°)= -cos30°= -(√3)/2   (30°-60°-90°, or 1-2-√3 triangle), sin90°=1, and

tan210°= tan(180°+30°)= tan30°= 1/√3 = (√3)/3  (30°-60°-90° triangle)  

The given equation is restated as follows:

2cos150°- 3sin90°+ tan210°= -2cos30°- 3sin90°+ tan30°

= -2(√3)/2 - 3(1) + (√3)/3 = -(9 + 2√3 )/3 (= approx. -4.1547)