Question

What is the difference between degrees and radians on the calculator and why do they affect the answers?

Answer 1

See below.

Explanation:

Radian and degree measurements are completely different from one another. Consider this:

`1^o= 57.2958` radians.

A calculator that does trig functions allows you to set it to degrees or radians for angular measurement. If you have it set for degrees and calculate say `sin 30` it will give you the result of `1/2`. If it is set for radians and you use `sin30` it will give you the result `~~-0.988040736`. This is because 30 radians is equal to `1718.87^o` NOT `30^o`. It is essential that you set the calculator to the correct unit of measurement first, or the results will be completely wrong.

Answer 2

see below

Explanation:

Degrees and radians are two different ways of measuring angles

Degrees:

degrees split a circle into 360 equal parts, so

`1^0=1/360th` of a circle

Radians

one radian is defined as the angle subtended at the centre of a circle by an arc length equal to that of the radius .

to convert between the two we use

`pi^c=180^0`

its value is `1^c~~57.29577...^0`

when dealing with questions involving trig always look for whether it is working in degrees or radians, and change the mode of your calculator accordingly.

In calculus we always working in radians because the standard results are only valid for radian measure.

eg

`d/(dx)(sinx)=cosx`