Use the given values to evaluate if possible all six trigono

Use the given values to evaluate (if possible) all six trigonometric functions. (If an answer is undefined, enter UNDEFINED.) tan x = 3, cos x = - 1/2

Solution

given tanx = sqrt(3) and cosx = -1/2

so tanx is positive and cosx is negative,

so x is in III (3rd) Quadrant

and cos x =-1/2

x = pi +pi/3

x=4pi/3

sinx = sin(4pi/3)

= - sqrt(3)/2

cscx = 1/sinx

= -2/sqrt(3)

secx = 1/cosx

= -2

cotx =1/tanx

= 1/sqrt(3)