Evaluate the six trigonometric functions at t = pi/6.

Question

Please help.

Answer 1

Construction of the angle produces a 30-60-90 triangle, which has angles and . From the above diagram, write for the vertical leg, then the horizontal leg is given by

by the Pythagorean theorem. Now use the double-angle formula

to obtain

which can be solved for to yield

Filling in the rest of the trigonometric functions then gives

 

Answer 2

t=π/6 Corresponds to the point (x,y)=(√3/2,1/2)

sin π/6 = y =1/2                                        cos π/6 =1/y = 1/1/2 =2

  cos π/6 = x =√3/2                                   sec π/6 =1/x = 2/√3 =2√3/3

tan π/6 = y/x = 1/2/√3/2 = 1/√3 = √3/3      cot π/6 = x/y = √3/2/1/2 = √3

 

Comments

sin π/6 = y =1/2                                        csc π/6 =1/y = 1/1/2 =2