Please solve stepbystepSolutionsin 08391cos 125 sin 08391

Please solve step-by-step.

Solution

sin + 0.8391cos = 1.25

sin + 0.8391(1 - sin²) = 1.25         since sin² + cos² = 1

==> 0.8391(1 - sin²) = 1.25 - sin

Squaring on both sides

==> [0.8391(1 - sin²)]² = (1.25 - sin)²

==> 0.70408881(1 - sin²) = 1.5625 + sin² - 2.5sin

==> 0.70408881 - 0.70408881sin² = 1.5625 + sin² - 2.5sin

==> 1.5625 + sin² - 2.5sin + 0.70408881sin² - 0.70408881 = 0

==> 1.70408881sin² - 2.5sin + 0.85841119 = 0

Using Quadratic formula

x = [-b + (b² - 4ac)]/(2(a)) , [-b - (b² - 4ac)]/(2(a))

sin = [-(-2.5)+((-2.5)² - 4(1.70408881)(0.85841119))]/(2(1.70408881)) ,[-(-2.5) -((-2.5)² - 4(1.70408881)(0.85841119))]/(2(1.70408881))

==> sin = [2.5+ 0.398764387 ]/3.40817762 , [2.5 - 0.398764387 ]/3.40817762

==> sin = [2.5+ 0.63147794 ]/3.40817762 , [2.5 - 0.63147794 ]/3.40817762

==> sin = 0.918813 , 0.5482467

==> = sin^-1(0.918813) , sin^-1(0.5482467)

==> = 1.1650625 , 0.58026634