Find the exact value of the cosine and sine of the following

Find the exact value of the cosine and sine of the following angle. theta = pi/6 cos(pi/6) = __________ sin (pi/6) = ____________

Solution

theta = pi/6

in a right angled triangle

theta = pi/6 = 30 degrees , one angle is 90 degrees and other is 60 degrees

so ratio of sides is sqrt 3 : 1 : 2

hence,

cos ( pi/6 ) = base / hypotenuse = sqrt 3/2

sin (pi/6 ) = perpendicular / hypotenuse = 1/2