Respuesta :

nuhulawal20

Answer:

the required positive radian measure of the smaller angle is 5π/6 radians or 2.618 radians

Step-by-step explanation:

Given the data in the question;

smaller angle formed by the hands of a  clock at 5 o'clock

{at 5 o'clock, two angles are form; 150° and 210°}

hence, the smaller angle is 150°

so, smaller angle = 150° × π/180°

smaller angle = 150°π/180°

smaller angle =  5π/6 radians or 2.618 radians

Therefore, the required positive radian measure of the smaller angle is 5π/6 radians or 2.618 radians

batolisis

The positive radian measure of the angle formed by the hands of the clock at 5 o'clock is [tex]\frac{5\pi}{6}\text{ radians}[/tex]

In one minute, the long hand makes a full turn equivalent to [tex]2\pi[/tex] radians.

At 1 o'clock, the smaller angle formed by the hands of the clock is

[tex]\dfrac{2\pi\text{ rads}}{12}=\dfrac{\pi}{6}\text{ rads}[/tex]

At 5 o'clock, the smaller angle is five times the one we have when the time is 1 o'clock. That is

[tex]\dfrac{\pi}{6}\text{ radians}\times 5=\dfrac{5\pi}{6}\text{ radians}[/tex]

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