What are the six trig function values of #pi/3#?

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Answer 1 · 2015-11-26T01:13:31

The #6# trigonometric values of #pi/3# are:

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

The #6# trigonometric ratios are:

#1. sintheta#
#2. costheta#
#3. tantheta#
#4. csctheta#
#5. sectheta#
#6. cottheta#

Using the ratios, we can determine their values when #theta# is #pi/3#:

Recall that #pi# radians is #180^@#.

#1. sintheta#

#=sin(pi/3)#

#=sin(180^@/3)#

#=sin(60^@)#

#=sqrt(3)/2#

#2. costheta#

#=cos(pi/3)#

#=cos(180^@/3)#

#=cos(60^@)#

#=1/2#

#3. tantheta#

#=tan(pi/3)#

#=tan(180^@/3)#

#=tan(60^@)#

#=sqrt(3)/1#

#=sqrt(3)#

#4. csctheta#

#=1/sintheta#

#=1/sin(pi/3)#

#=1/sin(180^@/3)#

#=1/sin(60^@)#

#=1/(sqrt(3)/2)#

#=2/sqrt(3)#

#=(2sqrt(3))/3#

#5. sectheta#

#=1/costheta#

#=1/cos(pi/3)#

#=1/cos(180^@/3)#

#=1/cos(60^@)#

#=1/(1/2)#

#=2#

#6. cottheta#

#=1/tantheta#

#=1/tan(pi/3)#

#=1/tan(180^@/3)#

#=1/tan(60^@)#

#=1/(sqrt(3)/1)#

#=1/sqrt(3)#

#=sqrt(3)/3#