A Math Question involving trig functions.

Find the values of the six trigonometric functions at each angle:

1.) 2π/3

How would i use this angle to find sin, cos, tan, cot, sec, and csc.?

THis angle is in quadrant 2, so sine and csc is positive, the rest of the functions are negative
π/3 or 60 degree is one of the special angle that you need to memorize
cos(2π/3) = -cos(π/3) = -cos(60 degree) = -1/2
sin(2π/3) = sin(π/3) = sin(60 degree) = sqrt(3)/2

tan(2π/3) = sin(60)/-cos(60) = - (1/2)/(sqrt(3)/2) = -sqrt(3)/3
cot(2π/3) = -cos(60)/sin(60) = 1/tan(2π/3) = sqrt(3)
sec(2π/3) = 1/cos(2π/3) = - 2sqrt(3)/3
csc(2π/3) = 1/sin(2π/3) = 2

Two ways:

1.) Change the mode of your calculator to radians and evaluate each function.

2.) Convert that angle to degrees using (1)rad=(180/pi)deg:

That would be multiply your angle times 180/pi, so (2pi/3)*(180/pi) the pi's cancel and you end up with 120 deg. From here evaluate each function.

You Evaluate each function using 2pi/3. For instance sin(2pi/3)= (3/4)^1/2

who knows