why, for the range 0<x<90, is sinx smaller than tanx ? thanks!?

Answer 1

Because if you look at it as a unit circle, with the radius moving from 0 to 90, you can see that the dominator of the sin is always the hypontenuse, but the denominator of the tangent is the adjacent side, and it is constantly shrinking.

So, while the Sin is moving toward 1, the tangent is diverging to infinity.

Answer 2

Where x is in degrees.

Tan x is sin x / cos x.

Cos of x from 0 to 90 ranges from 1 to 0. In other words, from 0 to 90, cos of x is less than 1.

Thus, for the range of 0 to 90, tan x is essentially sin x / (something from 0 to 1). Dividing a number by a number smaller than one generally results in a number larger than the original number.

IE: 1 / (.5) = 2, etc.

Hence, tan x is larger than sin x in the specified span.

Answer 3

the ratio of the opposite side to hypootenuse is sin x and the ratio of opp side by adj side is tanx
for the range 0 < x < 90 , as x increases form 0 to 90, the opposite side goes on increasing thehypotenuse remainig the same so by pythagorus theorem, if the opposite side increases, for a given hypotenuse, the adjacent side has to go on decreasing so tanx which has the adjacent side in the denominator goes on increasing resulting in sinx being smaller than tanx as x increases

Answer 4

In the range 0 < x < 90 , excluding 90, sin(x) is always smaller than tan(x). when x=0
sin(x)=tan(x)

Answer 5

because tanx =sinx/cosx and cosx value varies between 0 and 1 . so if you divide with a positive value less than 1 , then the dividend's value will be increased but not decreased.

Answer 6

write the question as:

why is sin(x)/ tan(x) < 1 in the given range?

Because this is same as sin(x)/[sin(x)/ cos(x)] = cos(x), which really is less than or equal to 1 form 0 to 90!

Answer 7

On that range, 0< cos(x) < 1, so 1/cos(x) > 1.

Also, on that range, sin(x) is positive, so multiplying 1/cos(x) > 1 by sin(x) we get

sin(x)/cos(x) > sin(x)

Thus, tan(x) > sin(x) for 0 < x < 90

Answer 8

tanx= sinx/cosx=3 sinx=3 cosx; sin^2x= 9 cos^2x sin^2x+cos^2x=a million 9 cos^2x+cos^2x =a million 10cos^2x=a million cos^2x=a million/10 cosx= + or - sqrt (a million/10) when you consider that x lies from ninety to 270 until ultimately one hundred eighty it is in the 2d quad sin perspective is +ve and from one hundred eighty to 270 it is in the 0.33 quad sin perspective is -ve so sinx =3cosx sinx= 3sqrt(a million/0) in the 2d quad sinx= -3sqrt(a million/10) in the 0.33 quad