Evaluate exactly all six trig functions of each of the following...

Question

1. All six trig functions of (2π)/3
2. All six trig functions of (11π)/4

Answer 1

(2(pi))/3 in radians is the same as 120 degrees using the pi radians = 180 degrees conversion

at 120 degrees the cos(120)= (1/2)

sin(120)= (sqrt(3))/2

tan(120)= (sqrt(3))

cot(120)= 1/(sqrt(3))= (sqrt(3))/3

sec(120)= 2

csc(120)=(2(sqrt(3)))/3

11pi/4 in radians is just 135 degrees since it rotates one full rotation about the positive x axis and then another 3pi/4 radians which is equal to 135 degrees using the conversion radians to degrees (pi radians = 180 degrees)

so

cos(135)= (sqrt(2))/2

sin(135)= (sqrt(2))/2

tan(135)= 1

cot(135) = 1

sec(135)= sqrt(2)

csc(135)= sqrt(2)