Question

If cos x = sin 200, find all possible values of x between -180 and 360

Answer 1

Answer:

-110 , 110 , 250

Step-by-step explanation:

If cos x = sin 200, find all possible values of x between -180 and 360

cos x = sin 200

=> Cosx = Sin(180 + 20)

=> Cosx = - Sin20

=> Cosx = -Sin(90 -70)

=> Cosx = -Cos70

x Lies in 2nd , 3rd Quadrants

=> Cosx   = Cos(180 ± 70)

=> cosx = Cos110  or Cos250

=> x = 110 or 250

Also Cos(-x) = Cosx

=> x = -110 also

all possible values of x between -180 and 360 =  -110 , 110 , 250

Answer 2

Answer:

x = -110 , 110 , 250

Step-by-step explanation:

cos x = sin 200 = sin(270-70)

cos x = -cos70 = cos(180-70) or cos(180+70) or cos(-180+70)

cos x = cos110 , cos250 , cos(-110)                             [because -180 < x < 360 ]

x = -110 , 110 , 250