Final answer:
To find all angles θ between 0° and 180° satisfying the equation sin(θ) = 7/9, use the inverse sine function (sin⁻¹) to determine these angles. The angles that satisfy the equation between 0° and 180° are approximately 44.4° and 135.6°.
Step-by-step explanation:
To find all angles θ between 0° and 180° satisfying the equation sin(θ) = 7/9, we need to use the inverse sine function (sin⁻¹) to determine these angles. The inverse sine function gives us the angle whose sine is equal to a given value. In this case, sin(θ) = 7/9, so we want to find the angle whose sine is equal to 7/9.
Using a calculator, we can find that sin⁻¹(7/9) ≈ 44.4°. However, we need to find all angles between 0° and 180°, so we need to consider the reference angle as well. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis in the standard position.
Since sine is positive in both the first and second quadrants, we add the reference angle to find the angles in the second quadrant. Therefore, the angles that satisfy the equation sin(θ) = 7/9 between 0° and 180° are approximately 44.4° and 135.6°.