Use a calculator to approximate the value of each expression. Give answers to six decimal places.sec 58.9041°

(Modeling) Fish's View of the World The figure shows a fish's view of the world above the surface of the water. (Data from Walker, J., 'The Amateur Scientist,' Scientific American.) Suppose that a light ray comes from the horizon, enters the water, and strikes the fish's eye.Assume that this ray gives a value of 90° for angle θ₁ in the formula for Snell's law. (In a practical situation, this angle would probably be a little less than 90°.) The speed of light in water is about 2.254 x 10⁸ m per sec. Find angle θ₂ to the nearest tenth.

(Modeling) Length of a Sag Curve When a highway goes downhill and then uphill, it has a sag curve. Sag curves are designed so that at night, headlights shine sufficiently far down the road to allow a safe stopping distance. See the figure. S and L are in feet. The minimum length L of a sag curve is determined by the height h of the car's headlights above the pavement, the downhill grade θ₁ < 0°, the uphill grade θ₂ > 0°, and the safe stopping distance S for a given speed limit. In addition, L is dependent on the vertical alignment of the headlights. Headlights are usually pointed upward at a slight angle α above the horizontal of the car. Using these quantities, for a 55 mph speed limit, L can be modeled by the formula (θ₂ - θ₁)S²L = ————————— , 200(h + S tan α)where S < L. (Data from Mannering, F., and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)Compute length L, to the nearest foot, if h = 1.9 ft, α = 0.9°, θ₁ = -3°, θ₂ = 4°, and S = 336 ft.

Use a calculator to approximate the value of each expression. Give answers to six decimal places.sec 222° 30'

Use a calculator to approximate the value of each expression. Give answers to six decimal places.tan 11.7689°

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places.cot θ = 1.1249386

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places.sec θ = 1.2637891

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places.csc θ = 9.5670466

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree.tan θ = 1.3763819