Solving trigonometric equations Solve the following equations.


sin²Θ = 1/4 , 0 ≤ Θ < 2π

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

cot (-17π/3)

Solving trigonometric equations Solve the following equations.

tan x = 1

Solving trigonometric equations Solve the following equations.

cos²Θ = 1/2 , 0 ≤ Θ < 2π

Solving trigonometric equations Solve the following equations.

sin Θ cos Θ = 0, 0 ≤ Θ < 2π

Area of a circular sector Prove that the area of a sector of a circle of radius r associated with a central angle $\theta$ (measured in radians) is $A=\frac12r^2\theta$.

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{Use of Tech} Launching a rocket A small rocket is launched vertically upward from the edge of a cliff $80$ ft above the ground at a speed of $96$ ft/s. Its height (in feet) above the ground is given by $h\left(t\right)=-16t^2+96t+80$, where $t$ represents time measured in seconds.

a. Assuming the rocket is launched at $t=0$, what is an appropriate domain for $h$?

Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of $10$ m² is filled to a depth of $25$ m with water. At $t=0$ s, a drain in the bottom of the tank with an area of $1$ m²  is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time $t\geq{0}$ is $d\left(t\right)=\left(5-0.22t\right)^2$.

a. Check that $d\left(0\right)=25$, as specified.

Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of $10$ m² is filled to a depth of $25$ m with water. At $t=0$ s, a drain in the bottom of the tank with an area of $1$ m²  is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time $t\geq{0}$ is $d\left(t\right)=\left(5-0.22t\right)^2$.

b. At what time is the tank empty?