Question

Through how many radians do the minute hand and the hourhand move between 1:00 p.m. and 1:45 p.m. (on the same day)?

Short answer

The angle that is moved by the minute hand is 4.7123 radian and the angler that is moved by the hour hand is 0.3927 radian.

Step-by-step solution

Step 1. Given Information.

Clocks and Angles In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through$\frac{1}{12}$ of a circle.

The time period is from 1 p.m. to 1:45 p.m.

Step 2. Write the concept.

Time t between 1:00 p.m. and 1:45 p.m.

$t=45min$

The hour hands moves$\frac{2\pi }{12}$ radians in 1 hr.

Step 3. Determining the values.

Since the minute hand moves the $2\pi$radian in 1 hr.

So,

role="math" localid="1648565748781" $\begin{array}{rcl}\text{Angle}& =& \frac{45}{60}\times 2\pi \\ & =& \frac{3\times 3.14}{2}\\ & =& 4.7123\text{radians}\end{array}$

Now,

The hour hand moves $\frac{2\pi }{12}$radians in 1 hr.

So,

$\begin{array}{rcl}\text{Angle}& =& \frac{45}{60}\times \frac{2\pi }{60}\\ & =& \frac{3.14}{8}\\ & =& 0.3927\text{radians}\end{array}$

Thus these are the values of angles moved by minute hand and hour hand.