Can you solve each equation to the nearest of a decimal, for 0<theta <360? 1) 4cos x+ √2=0 2）CSC x+3=0? Show all work

Answer 1

cscx + 3 = 0

1 4cosx + sqr2 = 0

4cosx =-sqr2

cosx = -(1/4)sqr2

use a calculator with an inverse trig function

x = about 180-69.3= 110.7 degrees

or 180+69.3 = 249.3 degrees

reference angle is 69.3 degrees

but cosines are negative only in quadrants II and III

solutions are 110.7 and 249.3 degrees

2 csc = -3

1/sinx =-3

sinx =-1/3

x = about 360- 19.47 = 340.53 degrees

or x= 180+19.47 = 199.47 degrees

reference angle = 19.47 degrees, but sines are negative only in quadrants III and IV