Hello, Confuzzled!

When 0 ≤ x ≤ 2π

. . a) . sin x .= .0.7

You need a calculator for this one.

. . x .= .Inverse sine of (0.7) .≈ .0.7754, 2.3662 radians.

When -π ≤ θ ≤ π

. . a) . 6sinθcosθ - 3cosθ + 2sinθ - 1 .= .0

Factor: . 3cosθ(2sinθ - 1) + (2sinθ - 1) .= .0

Factor: . (2sinθ - 1)(3cosθ + 1) .= .0

We have: . 2sinθ - 1 .= .0 . → . sinθ = 1/2 . → . θ .≈ .0.524, 2.618

. . . .and: . 3cosθ + 1 .= .0 . → . cosθ = -1/3 . → . θ .≈ .1.911, -1.911

When 0 ≤ θ ≤ 2π

. . b) . 3cos²θ - 13cosθ .= .sin²θ - 9

We have: . . . .3cos²θ - 13cosθ .= .1 - cos²θ - 9

. . .Then: . 4cos²θ - 13cosθ + 8 .= .0

This does not factor; we need the Quadratic Formula.

. . . . . . . . . . . . . . __

. . . . . . . . . .13 ± √41

. . cosθ . = . ----------- . ≈ . 2.4254, 0.8246

. . . . . . . . . . . . 8

We have: . cosθ .= .2.4254 . . . no solution!

. . . .and: . cosθ .= .0.8246 . → . θ .≈ .0.6013, 5.6819 radians