Question

Using the graph given solve the equations

(a) sinx- cosx =0
(b) sinx-cosx =0.5

Answer 1

a)

`\sin(x) - \cos(x) = 0`

`√(2) \sin(x - (\pi)/(4) ) = 0`

`x - (\pi)/(4) = 0`

`x = (\pi)/(4) \: radians = 45 \: degrees`

x = 45°

b)

`\sin(x) - \cos(x) = .5`

`√(2) \sin(x - (\pi)/(4) ) = (1)/(2)`

`\sin(x - (\pi)/(4) ) = ( √(2) )/(4)`

`x - (\pi)/(4) = {sin}^( - 1) ( √(2) )/(4)`

`x = (\pi)/(4) + {sin}^( - 1) ( √(2) )/(4) =1.15 \: radians = 65.70 \: degrees`

x = about 65.70°