Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

please explain elaborately the concept of quadrants the argument values assigned to each quadrant. how to apply this concept in inverse trigonometry?
Asked by anchaka | 10 May, 2013, 05:45: PM
answered-by-expert Expert Answer
While computing the inverse of any trignometric function, one needs to pay special attention to the sign of the number whose inverse is being carried out. 
 
For example, sin30 = sin 150 = 1/2 
However, cos30 = sqrt(3)/2 is not equal to cos150 = -sqrt(3)/2 and there is just a change of sign. 
 
So, if we need to determine sin^-1 (1/2), it can be anything, 30degree or 150 degree. 
However, if we are also given the corresponding cos^-1 value, then we can clearly say that in which quadrant it is. 
 
So, in the first quadrant i.e. x>=0 and y>=0; both sinA and cosA are positive and hence, tanA >0
in the second quadrant i.e. x<0 and y>=0; sinA is positive but cosA is negative and hence, tanA <0
in the third quadrant i.e. x<0 and y<0; both sinA and cosA are negative and hence, tanA >0
in the fourth quadrant i.e. x>=0 and y<0; sinA is negative however cosA is positive and hence, tanA < 0
 
This plays a major role when we try to find the argument in the case of complex numbers. So, argument = tan^-1 (y/x) for a complex number z = x+iy. 
 

Now, in the quadrants I and III, tan(t) is positive. In the quadrants II and IV, tan(t) < 0. In quadrant I,arg(z) = arctan(y/x). But, for quadrant III, the positive arctan(y/x) must be upgraded with the addition of pi. Similarly, for z in quadrant II, arctan(y/x) is negative. To bring it to the second quadrant we have to add pi. For z in the fourth quadrant, arctan(y/x) is again negative, but its location is correct. To keep it there we now have to add 2pi, so that the value falls into the interval[0, 2pi). To sum up, denote ?0 = tan(y/x). Then

 
arg(z) = ?0, x > 0, y > 0,
arg(z) = ?0 + pi, x < 0, y > 0,
arg(z) = ?0 + pi, x < 0, y < 0,
arg(z) = ?0 + 2pi   x > 0, y < 0,
Answered by | 11 May, 2013, 02:47: AM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Maths
solve it
question image
Asked by sahrudadayajena | 27 Jan, 2024, 09:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
tanx =3/4 and x lies in 3rd quadrant find sinx
Asked by rajashekararishu | 05 Jan, 2024, 09:31: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Solve for x : 2 tan−1 (cos x) = tan−1 (2 cosec x).
Asked by ambigamagendran256 | 04 Nov, 2023, 05:43: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
if sin x+2cos x=1 then find Tha value of 2sin x - cosx
Asked by gopalkumarrai87 | 11 Oct, 2023, 11:02: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
solve it
question image
Asked by sdmbotch1123 | 19 Sep, 2023, 01:53: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Solve it pls.
question image
Asked by sdmbotch1123 | 10 Apr, 2023, 10:55: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Evaluate 3 sin -1 (1/root 2) + 2 cos -1 (root3/2) + cos-1(0)
Asked by varma.renu9481 | 13 Mar, 2023, 11:51: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Sin^-1x = cos^-1x, 0<x<1. Solve  
question image
Asked by w3ctiger | 12 Feb, 2023, 11:55: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
tan¹x + tan¹y=π+tan¹(x+y/1-xy), xy>1;x, y>0
Asked by joymaibam38 | 26 Dec, 2021, 09:04: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
what is mateix
Asked by amansharma08116 | 14 Jul, 2021, 09:37: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×