indian jewelry wholesale new york Prove the size of X and SINX with text, let's describe it in detail, thank you!
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indian jewelry wholesale new york Prove the size of X and SINX with text, let's describe it in detail, thank you!
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miniature glass bottles jewelry wholesale Consider the scope of the positive number:
Is to imagine a fan -shaped with a radius of 1, the angle is 2x, and the arc length is 2X; on the other hand, SINX is a sideways on the side currency, that is, 1/2, which is 1/2 The strings length ratio is 1, and from the geometric figure, the half arc length X is obviously greater than the half string length. So x> sinx.
When using the strangeness, when the number is negative: x u003Csinx.
jewelry gift boxes wholesale canada This question was originally examined during the senior high school simulation examination. The original title was in the [-π/2, π/2] interval. Y = x and y = sin x had several intercourse points. One intersection. The translation of this question is that in the interval of [-π/2, π/2], except for x = 0, SINX = x, SINX, and X are big. At that time, many people did it wrong, and they chose 3. The teacher explained it. At that time, just say that drawing pictures, draw a little solution. Essence Essence
Now I want to understand how to do it. Only the unit is resolved. First, say [0, π/2] range, [-π/2, 0].
In the unit circle [0, π/2] interval, the SINX value is the vertical line perpendicular to the X axis, that is, the SIN line, this is easy to understand, what about X? Which line does it correspond to in the unit circle? (This problem is critical, and it is also to examine whether you can understand the unit circle and use the angle of π). X is an angle. We know that the 360 ° angle is represented by 2π in the unit circle, why is it 2π? Because in the unit circle with a radius of 1, the length of the circle is 2π, that is, the X -value corresponding to a circular arc length in the circle! Intersection Intersection
Then the 180 ° angle, in the unit circle, is the length of the semi -arc; the 90 ° angle is the length of the arc of 1/4, so that through the unit circle, we will unify the angle and circle. Essence Essence
It again to this question, [0, π/2] interval, except for X = 0, as long as the unit circle is rotated at 90 °, the arc length of the unit circle is always greater than the SIN line than the SIN line The straight line length, so in the [0, π/2] interval, SINX is always less than x, so that it can be extended to x from 0 to infinite large, SINX is always less than x
lula and lee jewelry wholesale 1. The general situation is very simple, you can know using function images or unit circles.
2. When X is close to 0, it is a good way to use the unit circle to process the triangle function.
I set A is the intersection of the unit circle and the X -axis. In the first quantity limit of the unit circle, the point B point B is a point on the unit circle. From the sine theorem, the area of the triangular OAB is (1*1*sinx)/2 = sinx/2; the area of the fan OAB is (1*x)/2 = x/2 (this is half of the arc and radius). Obviously, SINX u003Cx is considered from the area.
3. If the vertical line of point A is used as an X -axis from point A in the graph above, and OB intersects to point C, then AC = TANX, which also uses the area relationship to obtain the unequal Sinx u003Cx u003Ctanx
4 If further simplification, when X tends to 0, X and SINX can be regarded as equal. In other words, the limit of SINX/X at 0 is 1.
5. In high mathematics, according to the principle of changing the two generations of infinite small generations, x, sinx, tanx can be replaced by each other, which can be regarded as equal. (Note: Under the circumstances of 0.)