We've already looked at how to find angles using trigonometric ratios and we are used to giving our answers as whole numbers or decimals. Now we are going to look at another way to express a part of a degree using minutes and seconds.
There are $60$60 minutes in $1$1 degree.
There are $60$60 seconds in $1$1 minute.
To convert a decimal into minutes and seconds, we need to find what decimal
For example, let's say we wanted to round $15.72^\circ$15.72° to the nearest minute.
We need to work out $15^\circ$15° + $0.72$0.72 of a degree, which is $15^\circ$15° + $0.72$0.72 of a $60$60 minutes.
$0.72\times60$0.72×60 | $=$= | $43.2$43.2 minutes |
So, $15.72^\circ$15.72° rounded to the nearest minute is $15^\circ$15°$43$43'.
There are also some buttons our your calculator to help you work with minutes and seconds.
The button highlighted in blue allows you to write degrees and minutes in your calculator.
The button highlighted in green will convert between decimals and minutes/seconds.
Rounding minutes and seconds is similar to rounding decimals. However, because there are $60$60 minutes in a degree and $60$60 seconds in a minute, our half way point is $30$30.
If the seconds are $30$30 or above, we round up to the nearest minute.
Round $25^\circ$25°$49$49'$40$40" to the nearest minute.
$\editable{}$° $\editable{}$'
Convert the following into degrees and minutes:
$24.4^\circ$24.4°=$\editable{}$ degrees $\editable{}$ minutes
Given $10\cos x=7$10cosx=7:
Find the value of $x$x correct to two decimal places.
Hence find $x$x to the nearest minute.
Consider the following diagram.
Find the value of $x$x correct to 2 decimal places.
Hence find $x$x to the nearest minute.
Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions
Apply trigonometric relationships in solving problems