MATH 2422 #4: QUESTION 2

#4: 2a) ANSWER: Þ ² ( 2 cos ² 0 + 3 sin ² 0 - 4 cos ² ø ) + Þ sinø cos0 = 5
SOLUTION: 2( Þ sinø cos0 ) ² + 3( Þ sinø sin0 ) ² - 4( Þ cosø ) ² + ( Þ sinø cos0 ) = 5
Þ ² ( 2 cos ² 0 + 3 sin ² 0 - 4 cos ² ø ) + Þ sinø cos0 = 5

#4: 2c) ANSWER: Þ = 8 / (sinø cos0 + 2 sinø sin0 + 3 cosø )
SOLUTION: Þ sinø cos0 + 2Þ sinø sin0 + 3Þ cosø = 8 or Þ = 8 / (sinø cos0 + 2 sinø sin0 + 3 cosø )

#4: 2e) ANSWER: ø = + pi / 4
SOLUTION: ( Þ sinø cos0 ) ² + ( Þ sinø sin0 ) ² - ( Þ cosø ) ² = 0 or
sin ² ø cos ² 0 + sin ² ø sin ² 0 - cos ² ø = 0 or
sin ² ø = cos ² ø or tan ø = + 1 or ø = + pi / 4