use the fundamental identities to find the values of the 6 trig functions of the given conditions. Sinθ=2/5 and cosθ<0

Answer 1

sinx = 2/5 = opposite side over hypotenuse

the angle whose sine = 2/5 is in either the 2nd or 1st quadrant

cosine is negative in only the 2nd or 3rd quadrant

cosx = adjacent side over hypotenuse = -sqr(25-4)/5 = -sqr21/5

the angle is in the 2nd quadrant, as that's the only quadrant where cosx<0 and sinx>0

secx= inverse of cosx = -5/sqr21

cscx = inverse of sinx = 5/2

tanx = opposite over adjacent = -2/sqr21

cotx = inverse of tanx = -sqr21/2

sqr21 = approximately 4.58

so rounded to 2 digits

sinx=2/5= 0.40

cosx =-4.58/5 = -0.92

cscx =5/2 = 2.50

secx = -5/4.58 = - 1.09

tanx = -2/4.58 =-0.44

cotx = -4.58/2 = -2.29