Question

lim sinx degree / x​

Answer 1

Answer:

sinx=p/h

Step-by-step explanation:

please Mark as brainliest and follow

Answer 2

Here’s a conceptual way to think about it.

Consider the derivative of sin()
sin
⁡
(
x
)
evaluated at =0
x
=
0
radians. The definition of the derivative tells us that this derivative is given by:

lim→0sin(0+)−sin(0)=lim→0sin
lim
x
→
0
sin
⁡
(
0
+
x
)
−
sin
⁡
(
0
)
x
=
lim
x
→
0
sin
⁡
x
x


So the limit you are asking about is really a derivative, and a derivative is really just a rate of change. Specifically, the derivative measures how fast sin()
sin
⁡
(
x
)
changes compared to how fast
x
changes when
x
is at zero.

You rightly state that that answer is 1. In other words, at =0
x
=
0
the sine function changes at exactly the same rate as
x
.

But what if we measure
x
in degrees? Well, radians are A LOT bigger than degrees since 360 degrees is the same as 2
2
π
(about 6.28 ) radians. So since the sine function changes at the same rate as
x
when
x
is measured in radians, it CANNOT possibly change at the same rate as
x
when
x
is measured in degrees. Why not?

Well, a change of 1 degree corresponds to a change of 180
π
180
radians. So if we change
x
by 180
π
180
radians, we expect the sine function to change by about 180
π
180
. That’s what the derivative being equal to one means. But that means the sine function changes by about 180
π
180
when
x
changes by 1 degree. So if we are measuring in degrees, we see that the rate of change is no longer 1 but rather much less: 180.
π
180
.


And that’s why the first limit is one while the second is 180
π
180
.