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Solve the Problem θ\theta , the Water Level L Behind the Wheel Changes According

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Essay

Solve the problem.
-A water wheel rotates through the angle θ\theta , the water level L behind the wheel changes according to the equation L=1sinθ2cos2θ\mathrm { L } = 1 - \sin \theta - 2 \cos ^ { 2 } \theta where L is measured in inches. Determine the values of θ\theta for which the water level is zero. Find the exact values.
Do not use a calculator.

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Definitions:

Hornfels

A fine-grained metamorphic rock formed by the contact metamorphism of shale and other clay-rich rocks.

Foliation

The repetitive layering in metamorphic rocks, which occurs due to the reorientation of minerals under intense heat and pressure.

Thrust Fault

a type of reverse fault where the upper block, above the fault plane, moves up and over the lower block.

Metamorphic Rock

rock that has undergone transformation from an original form due to high pressure, high temperature, or both.

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