IIT JEE , AIEEE Forum - Mathematics , Trignometry - trigonometric ratios with the help of unit circle

sinjan.j

please read carefully

let us take a graph sheet(look at fig 1)

now we draw a unit circle on top of the graph sheet(look at fig 2)

if any angle is present in quadrant 1 the angle will be between 0 to 90 degrees.

in case of any angle

cos

=x and

sin

=y.

so in case of 0 degrees

sin

=y=0

cos

= x = 1

therefore tan

=sin

/cos

=0/1=0

but think of cot

= 1/tan

=1/0 (which is not defined)

so why do we say that all the ratios in the first quadrant is positive??

nivedh_89

1st quadrant includes all the angles between 0 to 90.........!!!!!!!!!!!!!
i dont think 0 is included....................it lies on the X-axis...............!!!!!!!!

srujana

nivedh is right

jatinroxx

Here

= 0 represents the X - axis...

It is the line dat separates the halves......

It is not a part of the quadrant.....

More specifically speaking,

Domain of cot

is R - (n pi)......

iitkgp_bipin

1st quadrant is between 0 and 90.
Actually at 0 the quadrant changes and theta=0 separates the quadrants. Similarly for theta=90.

sinjan.j

i more thing is that

in first quadrant tan value increases from 0 to

(90 degrees)

but in the second quadrant why the tan value increases from - to 0??

please explain!!

jatinroxx

'coz its discontinuous................

tan @ = sin@/cos@

At @ approaching pi/2 from left, cos @ approaches 0 from right or 0⁺

At @ approaching pi/2 from right, cos @ approaches 0 from left or 0^-

Hence the discontinuity.......

sinjan.j

but jatin i am still getting confused.

just explain more clearly.

avinash.sharma

Dear sinjan.j and All other trigo. lovers.

There is a periodic movement in the value of Sin & Cos. From 0 to 360 drgree Sine moves 0 to 1, 1 to 0, 0 to ?1 and than ?1 to 0. Sameway the movement of Cos but with a difference. See the table below for details.

Angle	Movement of Sin	Movement of Cos	Resulting Movement of Tan
B/w 0 - 90	+ ve (0 to 1) Increasing	+ ve ( 1 to 0) Decreasing	+ ve
B/w 90-180	+ ve ( 1 to 0) Decreasing	- ve ( 0 to ?1) Decreasing	- ve
B/w 180- 270	- ve ( 0 to ?1) Decreasing	- ve ( -1 to 0) Increasing	+ ve
B/w 270 -360	- ve ( -1 to 0) Increasing	+ ve ( 0 to 1) Increasing	- ve

Due to this the sign of Tan in first quadrant is 0 to but in second quadrant is - to 0

See the detail values:

Angles	SIN	COS	TAN
0	0.00	1.00	0.00
15	0.26	0.97	0.27
30	0.50	0.87	0.58
45	0.71	0.71	1.00
60	0.87	0.50	1.73
75	0.97	0.26	3.73
90	1.00	0.00	-
105	0.97	-0.26	-3.73
120	0.87	-0.50	-1.73

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