How can I find the angular position in radians of the minute hand of a clock at 5:00, 7:15, an 3:35?

a) 5:00
At 00 minutes, the minute hand is point straight up. That is one quarter turn of the entire circle. One-fourth of 2π radians is 1/2 π, or π/2

b) 7:15
At 15 minutes, the minute hand is pointing straight to the right, along the imaginary positive x-axis, so it has turned through none of the circle. 0 radians.

c) 3:30
This one isn't as clean as the others. Let's first find the 35 minute position: it occurs at hour number 7. Identify that measuring from 3 (positive x-axis, measuring counter clockwise) you have to turn through 40 minutes worth of clock. 40 minutes represents 40/60 of an entire clock, which reduces to 2/3. 2/3 of all the radians in a circle (2π of them) is 4/3π, or 4π/3.

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psm22415 psm22415 · Answer 2 · 2022-02-04T07:45:56+01:00

The angular position of the minute hand at 3:35 is 3.66 radian.

The angular position of the minute hand at 7;15 is 0 radian.

The angular position of the minute hand at 5;00 is 1.57 radian.

What is the angular position in radians of the minute hand of a clock?

The angular velocity can be defined as the rate of the angular position of the rotating body.

The rate of rotation around an axis is usually expressed in the radians or revolutions per second or per minute.

1. The angular position of the minute hand at 5:00 is 90 °.

Convert degrees into radians.

Multiply by π/180 degrees.

[tex]\rm =90 \times \dfrac{\pi }{180}\\\\= \dfrac{\pi }{2}\\\\= 1.57 \ radian[/tex]

The angular position of the minute hand at 5;00 is 1.57 radian.

2. The angular position of the minute hand at 7;15 is 0°.

At 15 minutes, the minute hand is pointing straight to the right, along the imaginary positive x-axis, so it has turned through none of the circles.

The angular position of the minute hand at 7;15 is 0 radian.

3. The angular position of the minute hand at 3:35 is 7π/6.

The angular position of the minute hand at 3:35 is 210°.

The angular position of the minute hand at 3:35 is 3.66 radian.

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https://brainly.com/question/408236