Sec x =4 and sin x<0

Question

Use the fundamental identities or sketch a triangle to evaluate the other 5 trigonometric functions.

Answer 1

the angle is in quadrant IV. sinx<0, so that eliminates quadrants I and I.

secx>0 so that eliminates quadrant III, leaving only quadrant IV

secx=4 = hypotenuse/adjacent side= 1/(1/4) adjacent side=1/4

opposite side = -sqr(1^2 - (1/4)^2) = -sqr(1-1/16) = -sqr(15/16) =(-1/4)sqr15=

-(sqr15)/4

cosx =1/secx = 1/4

sinx = opposite side over hypotenuse = -(sqr15)/4

cscx = 1/sinx = -4/sqr15

tanx = sinx/cosx = opposite side/adjacent side = -(sqr15)/4/1/4 = -sqr15

cotx =1/tanx = -1/sqr15