find the exact values of the six trig functions of theta equals six pi divided by 8

Answer 1

6π/8 radians = 135°
135° is in quadrant II
The reference angle of 135° is 45°
45° is found in the 1-1-√2 right-angled triangle
In quadrant II , the sine and cosecant are positive

so
sin (6π/8) = 1/√2 , csc (6π/8) = √2
cos (6π/8) = -1/√2 , sec (6π/8) = -√2
tan (6π/8) = -1 , cot (6π/8) =-1