I need help with these 3-word problems for my trigonometry homework. Please explain how you got the answer and any work.

9514 1404 393

Step-by-step explanation:

The applicable relation in each case is ...

  s = rθ

where s is arc length, r is radius, and θ is rotation angle in radians. Of course the relation between degrees and radians is that π radians = 180°.

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1. s = (1.5 m)(302.2/180π) ≈ 7.91 m

About 7.91 meters of wire will be wound on the drum.

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2. The area of a sector is found by a formula that is similar to that for the area of a triangle. For a triangle, the area is A=1/2bh, where b is the base length and h is the height of the triangle. For a sector, the area is A=1/2sr, where s is the arc length and r is the radius. Usually, this is put in the form ...

  A = 1/2sr = 1/2(rθ)r

  A = 1/2r²θ

The angle through which the pendulum sweeps is ...

  (9°/s)(4 s) = 36° = (36°/180°)π radians = π/5 radians

Then the swept area is ...

  A = 1/2(14 cm)²(π/5) = 19.6π cm² ≈ 61.58 cm²

Each complete right to left swing sweeps an area of about 61.58 cm².

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3. Each rotation is 2π radians of angle, so the angular speed is ...

  angle/time = (2π radians/revolution)(17 revolutions)/(32 s) = 17/16π radians/s

  ≈ 3.34 radians/s

The distance covered per unit time is found using the arc length formula above.

 (arc length)/time = (rθ)/time = (25 cm)(17/16π rad/s)

 = (426/16)π cm/s ≈ 83.45 cm/s . . . . . pulley rim speed