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

1 Answer
Nov 26, 2015

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

Explanation:

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