Trig Functions

Question

Find exact solutions of √2sin (x- pi/4) +1 =0,  0 ≤x ≤ 3 pi

Answer 1

√2sin(x-45º)+1=0

√2sin(x-45º)=-1

sin(x-45º)=-1/√2

-1/√2=-√2/2

look on the unit circle and find, in the third and fourth quadrants, -√2/2 for the sine

sin of 5∏/4=-√2/2

5∏/4=225º

x-45º=225º

x=225º+45º

x=270º

 

sin of 7∏/4=-√2/2

7∏/4=315º

x-45º=315º

x=315º+45º

x=360º

Answer 2

(√2)sin (x- pi/4) +1 =0

sin(x-pi/4) = -1/√2

 

Within the interval 0≤x≤3pi, this occurs when (x-pi/4) = 5pi/4 and (x-pi/4) = 7pi/4.  Solve for x.