In a right angle triangle solve the expression sinpi6 cosp

In a right angle triangle solve the expression : sinpi/6 - cospi/3 .

Solution

In a right angle triangle, where one cathetus is b and the other one is c and the hypothenuse is a, a cathetus opposite to the angle pi/6 (meaning 30 degrees) is half from hypothenuse.

If b is the opposite cathetus to pi/6 angle, that means that b=a/2. In this way, we can find the other cathetus length, using Pythagorean theorem.

a^2=b^2 + c^2

a^2 = a^2/4 + c^2

a^2 - a^2/4 = c^2

3a^2/4 = c^2

[a(3)^1/2]/2=c

sin pi/6=opposite cathetus/hypotenuse

sin pi/6= (a/2)/a

sin pi/6=1/2

cos pi/3=cos 60=adjacent cathetus/hypotenuse

cos pi/3= (a/2)/a

cos pi/3=1/2

sin pi/6 - cos pi/3=1/2 -1/2=0