show your workSolution10sin2t 9sint 7 0 u sint 10u2 9u

show your work

Solution

10sin²t + 9sint - 7 = 0

u = sint

==> 10u² + 9u - 7 = 0

==> 10u² + 14u - 5u - 7 = 0

==> 2u(5u + 7) - 1(5u + 7) = 0

==> (2u - 1)(5u + 7) = 0

==> u = 1/2 , u = -7/5

==> sint = 1/2 , sint = -7/5

the range of sine function is [-1 , 1] and as -7/5 is not in the range , sint cannot be equal to -7/5

==> sint = 1/2

Given interval is [90 , 270]

sine function is positive in second quadrant

==> sint = 1/2

==> t = 180 - sin^-1(1/2)

==> t = 180 - 30 = 150

Hence t = 150