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

+2 votes
Please help.
asked Mar 1, 2013 in TRIGONOMETRY by andrew Scholar

2 Answers

+2 votes

Construction of the angle pi/6=30 degrees produces a 30-60-90 triangle, which has angles theta=pi/6 and 2theta=pi/3. From the above diagram, write y=sintheta for the vertical leg, then the horizontal leg is given byx=sqrt(1-y^2)=sin(2theta)

by the Pythagorean theorem. Now use the double-angle formulasin(2theta)=2sinthetacostheta

to obtainsqrt(1-y^2)=2ysqrt(1-y^2),

which can be solved for y=sintheta to yieldsintheta=1/2.

Filling in the rest of the trigonometric functions then gives

cos(pi/6) = 1/2sqrt(3)
cot(pi/6) = sqrt(3)
csc(pi/6) = 2
sec(pi/6) = 2/3sqrt(3)
sin(pi/6) = 1/2
tan(pi/6) = 1/3sqrt(3).

 

answered Mar 1, 2013 by kevin Rookie
0 votes

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

 

answered Mar 2, 2013 by steve Scholar
sin π/6 = y =1/2                                        csc π/6 =1/y = 1/1/2 =2

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