Evaluate the 6 trig functions for given angles

Question

1) 0 = 11pi/ 6

sin0 =

cos 0 =

tan 0 =

csc 0 =

sec 0 =

cot 0 =

2) 0 = 225 degree

sin0 =

cos 0 =

tan 0 =

csc 0 =

sec 0 =

cot 0 =

3) 0 = 2pi/ 3

sin0 =

cos 0 =

tan 0 =

csc 0 =

sec 0 =

cot 0 =

5) 0 = 175 degree

sin0 =

cos 0 =

tan 0 =

csc 0 =

sec 0 =

cot 0 =

4) 0 = -pi/2

sin =

cos =

tan =

csc =

sec =

cot =

Answer 1

I’ll help with number 1:

11π/6 = -π/6 so it’s in Quadrant 4

Only cosine is positive in Q4

The reference angle is π/6 or 30°

sin(π/6) = 1/2, so

sin (11π/6) = -1/2

cos(π/6) = √3/2, so

cos(11π/6) = √3/2

tan(π/6) = 1/2 / √3/2 = 1√3 = √3/3, so

tan(11π/6) = -√3/3

csc(11π/6) = the reciprocal of sin(11π/6), so

csc(11π/6) = -2

sec(11π/6) = the reciprocal of cos(11π/6), so

sec(11π/6) = 2√3 /3

cot(11π/6) = the reciprocal of tan(11π/6), so

cot(11π/6) = -√3