How do you find the exact value of all 6 trigonometric functions for the angle pi/6?
1 Answer
Construct a right angled triangle with angles
Explanation:
Consider an equilateral triangle with sides of length
Bisect it to make two right angled triangles, with sides of length
The smallest angle of one of these right angled triangles will be
Hence:
#sin (pi/6) = 1/2# (from: sin = opposite/hypotenuse)
#cos (pi/6) = sqrt(3)/2# (from: cos = adjacent/hypotenuse)
#tan (pi/6) = 1/sqrt(3)# (from: tan = opposite/adjacent)
Then the reciprocal trig functions:
#csc (pi/6) = 1/sin (pi/6) = 2/1 = 2#
#sec (pi/6) = 1/cos (pi/6) = 2/sqrt(3)#
#cot (pi/6) = 1/tan (pi/6) = sqrt(3)/1 = sqrt(3)#