What is the exact value of ([sin ((3pi)/2) + sec (-855°)] [cos(-5pi) + tan(1080°)] )/( [cot (2pi)/3 + sec(-330°)] tan (8pi)/3 + csc 945°)?

1 Answer
May 21, 2015

Let's start by the radians. Just remember that 360º=2pi, so whenever is written in function of pi follows this proportion; for example, pi=180º because it's half that measure and so on.

(I'll adopt three decimals, ok?)

sin((3pi)/2)=sin((3*180º)/2)=sin(270º)=-0.176

cos(-5pi)=cos(-5*180º)=cos(-900º)=cos(-900+360º+360º+360º)=cos(180º)=-0.598

(cot(2pi))/3=(cot(360º))/3=(-0,296)/3=0.099

tan(8pi)/3=tan(1440)/3=2.238/3=0.746

Now, the degrees:

sec(-855º)=sec(-855+360+360+360)=sec(225)=2.722

tan(1080º)=-0.856

sec(-330º)=sec(-330+360)=6.483

csc(945º)=1.722

Now, let's just substitute them!

((-0.176+2.722)(-0.598+0.856))/((0.099+6.483)0.746+1.722)

(2.546*0.258)/(4.910+1.722)=0.657/6.632=0.099

Just remembering: I consisdered only three decimal digits, so this answer is not precise.