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phinah 26 Apr 2018, 19:32
You state in Section four that all angles are in radians and that the formulas do not work in degress.
Why do they only work in radians?
4. Integration: Basic Trigonometric Forms
Just wanted to know if there are some integration techniques that work in degrees.
X
You state in Section four that all angles are in radians and that the formulas do not work in degress. Why do they only work in radians?
Relevant page <a href="https://www.intmath.com/methods-integration/4-integration-trigonometric-forms.php">4. Integration: Basic Trigonometric Forms</a> What I've done so far Just wanted to know if there are some integration techniques that work in degrees.
Murray 26 Apr 2018, 22:03
Radians have the "magical" quality that they can act as angles (amount of turn around a point) or as number quantities (the quality that allows us to use them in calculus).
Degrees, on the other hand, can only be a measure of an angle (or of course, temperature).
Probably the best way to show why degrees don't work in calculus is through an example. We'll look at it from the differentiation point of view.
Consider this graph which shows `y=sin(x)` using radians (in green) and using degrees (in magenta):
We know the following for the green curve:
`d/dx sin(x) = cos(x)`
At `x=0`, the slope is `cos(0) = 1`
But now consider the slope of the magenta curve (using degrees). It is much less, and in fact it is:
At `x=0^@`, the slope is `pi/180 cos(0^@) = pi/180`
So if we wanted to use degrees for calculus, we would have to multiply a lot of our expressions by `pi/180` (or similar) and it would get very messy.
In order for the following formula to "work", `x` needs to be in radians:
`d/dx sin(x) = cos(x)`
Hope it helps.
X
Radians have the "magical" quality that they can act as angles (amount of turn around a point) or as number quantities (the quality that allows us to use them in calculus). Degrees, on the other hand, can only be a measure of an angle (or of course, temperature). Probably the best way to show why degrees don't work in calculus is through an example. We'll look at it from the differentiation point of view. Consider this graph which shows `y=sin(x)` using radians (in green) and using degrees (in magenta): [graph]310,250;-1,10;-1.1,1.1,1.57,1;sin(x),sin(3.14x/180)[/graph] We know the following for the green curve: `d/dx sin(x) = cos(x)` At `x=0`, the slope is `cos(0) = 1` But now consider the slope of the magenta curve (using degrees). It is much less, and in fact it is: At `x=0^@`, the slope is `pi/180 cos(0^@) = pi/180` So if we wanted to use degrees for calculus, we would have to multiply a lot of our expressions by `pi/180` (or similar) and it would get very messy. In order for the following formula to "work", `x` needs to be in radians: `d/dx sin(x) = cos(x)` Hope it helps.
X
It does. A good example to use. Thank you.
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